SSAT Upper Level Math : Coordinate Geometry

Study concepts, example questions & explanations for SSAT Upper Level Math

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Example Questions

Example Question #291 : Coordinate Geometry

What coordinate point is the black circle on? 

Screen shot 2015 07 29 at 4.25.25 pm

Possible Answers:

\(\displaystyle (15,11)\)

\(\displaystyle (1,13)\)

\(\displaystyle (0,0)\)

\(\displaystyle (12,17)\)

\(\displaystyle (8,19)\)

Correct answer:

\(\displaystyle (15,11)\)

Explanation:

To find the location on a coordinate plane we first look at the \(\displaystyle x\)-axis, which runs horizontal and then the \(\displaystyle y\)-axis, which runs vertical. We write the point on the \(\displaystyle x\)-axis first, followed by the point on the \(\displaystyle y\)-axis. \(\displaystyle (x,y)\)

The black circle is over \(\displaystyle 15\) on the \(\displaystyle x\)-axis and up \(\displaystyle 11\) on the \(\displaystyle y\)-axis. 

Example Question #292 : Coordinate Geometry

What coordinate point is the orange triangle on? 


Screen shot 2015 07 29 at 4.25.25 pm

Possible Answers:

\(\displaystyle (14,18)\)

\(\displaystyle (15,17)\)

\(\displaystyle (19,21)\)

\(\displaystyle (13,1)\)

\(\displaystyle (17,4)\)

Correct answer:

\(\displaystyle (17,4)\)

Explanation:

To find the location on a coordinate plane we first look at the \(\displaystyle x\)-axis, which runs horizontal and then the \(\displaystyle y\)-axis, which runs vertical. We write the point on the \(\displaystyle x\)-axis first, followed by the point on the \(\displaystyle y\)-axis. \(\displaystyle (x,y)\)

The orange triangle is over \(\displaystyle 17\) on the \(\displaystyle x\)-axis and up \(\displaystyle 4\) on the \(\displaystyle y\)-axis. 

Example Question #293 : Coordinate Geometry

What coordinate point is the green triangle on? 


Screen shot 2015 07 29 at 4.25.25 pm

Possible Answers:

\(\displaystyle (15,6)\)

\(\displaystyle (17,18)\)

\(\displaystyle (21,7)\)

\(\displaystyle (14,3)\)

\(\displaystyle (21,9)\)

Correct answer:

\(\displaystyle (21,9)\)

Explanation:

To find the location on a coordinate plane we first look at the \(\displaystyle x\)-axis, which runs horizontal and then the \(\displaystyle y\)-axis, which runs vertical. We write the point on the \(\displaystyle x\)-axis first, followed by the point on the \(\displaystyle y\)-axis. \(\displaystyle (x,y)\)

The green triangle is over \(\displaystyle 21\) on the \(\displaystyle x\)-axis and up \(\displaystyle 9\) on the \(\displaystyle y\)-axis. 

Example Question #294 : Coordinate Geometry

What coordinate point is the blue circle on? 


Screen shot 2015 07 29 at 4.25.25 pm

Possible Answers:

\(\displaystyle (17,6)\)

\(\displaystyle (5,17)\)

\(\displaystyle (24,16)\)

\(\displaystyle (3,3)\)

\(\displaystyle (8,9)\)

Correct answer:

\(\displaystyle (24,16)\)

Explanation:

To find the location on a coordinate plane we first look at the \(\displaystyle x\)-axis, which runs horizontal and then the \(\displaystyle y\)-axis, which runs vertical. We write the point on the \(\displaystyle x\)-axis first, followed by the point on the \(\displaystyle y\)-axis. \(\displaystyle (x,y)\)

The blue circle is over \(\displaystyle 24\) on the \(\displaystyle x\)-axis and up \(\displaystyle 16\) on the \(\displaystyle y\)-axis. 

Example Question #295 : Coordinate Geometry

What coordinate point is the red circle on? 


Screen shot 2015 07 29 at 4.25.25 pm

Possible Answers:

\(\displaystyle (16,17)\)

\(\displaystyle (30,6)\)

\(\displaystyle (8,17)\)

\(\displaystyle (6,30)\)

\(\displaystyle (17,8)\)

Correct answer:

\(\displaystyle (30,6)\)

Explanation:

To find the location on a coordinate plane we first look at the \(\displaystyle x\)-axis, which runs horizontal and then the \(\displaystyle y\)-axis, which runs vertical. We write the point on the \(\displaystyle x\)-axis first, followed by the point on the \(\displaystyle y\)-axis. \(\displaystyle (x,y)\)

The red circle is over \(\displaystyle 30\) on the \(\displaystyle x\)-axis and up \(\displaystyle 6\) on the \(\displaystyle y\)-axis. 

Example Question #296 : Coordinate Geometry

Starting at the coordinate point shown below, if you move up \(\displaystyle 10\) and to the right \(\displaystyle 9\), what is your new point? 

Screen shot 2015 07 30 at 8.51.14 am

Possible Answers:

\(\displaystyle (13,13)\)

\(\displaystyle (15,15)\)

\(\displaystyle (16,16)\)

\(\displaystyle (12,12)\)

\(\displaystyle (14,14)\)

Correct answer:

\(\displaystyle (12,12)\)

Explanation:

The starting point is at \(\displaystyle (3,2)\). When we move up or down we are moving along the \(\displaystyle y\)-axis. When we move to the right or left we are moving along the \(\displaystyle x\)-axis. 

Moving up the \(\displaystyle y\)-axis and moving right on the \(\displaystyle x\)-axis means addition. 

Moving down the \(\displaystyle y\)-axis and moving left on the \(\displaystyle x-\)axis means subtraction. 

Because we are moving up \(\displaystyle 10\), we can add \(\displaystyle 10\) to our \(\displaystyle y\) coordinate point and because we are moving to the right \(\displaystyle 9\) we can add \(\displaystyle 9\) to our \(\displaystyle x\)coordinate point. 

\(\displaystyle 2+10=12\)

\(\displaystyle 3+9=12\)

\(\displaystyle (12,12)\)

Example Question #297 : Coordinate Geometry

Starting at the coordinate point shown below, if you move up \(\displaystyle 2\) and to the right \(\displaystyle 8\), what is your new point? 


Screen shot 2015 07 30 at 8.51.14 am

Possible Answers:

\(\displaystyle (3,7)\)

\(\displaystyle (11,4)\)

\(\displaystyle (4,11)\)

\(\displaystyle (7,3)\)

\(\displaystyle (12,5)\)

Correct answer:

\(\displaystyle (11,4)\)

Explanation:

The starting point is at \(\displaystyle (3,2)\). When we move up or down we are moving along the \(\displaystyle y\)-axis. When we move to the right or left we are moving along the \(\displaystyle x\)-axis. 

Moving up the \(\displaystyle y\)-axis and moving right on the \(\displaystyle x\)-axis means addition. 

Moving down the \(\displaystyle y\)-axis and moving left on the \(\displaystyle x-\)axis means subtraction. 

Because we are moving up \(\displaystyle 2\), we can add \(\displaystyle 2\) to our \(\displaystyle y\) coordinate point and because we are moving to the right \(\displaystyle 8\) we can add \(\displaystyle 8\) to our \(\displaystyle x\)coordinate point. 

\(\displaystyle 2+2=4\)

\(\displaystyle 3+8=11\)

\(\displaystyle (11,4)\)

Example Question #298 : Coordinate Geometry

Starting at the coordinate point shown below, if you move up \(\displaystyle 6\) and to the right \(\displaystyle 4\), what is your new point? 


Screen shot 2015 07 30 at 8.51.14 am

Possible Answers:

\(\displaystyle (7,8)\)

\(\displaystyle (11,10)\)

\(\displaystyle (9,10)\)

\(\displaystyle (14,13)\)

\(\displaystyle (12,13)\)

Correct answer:

\(\displaystyle (7,8)\)

Explanation:

The starting point is at \(\displaystyle (3,2)\). When we move up or down we are moving along the \(\displaystyle y\)-axis. When we move to the right or left we are moving along the \(\displaystyle x\)-axis. 

Moving up the \(\displaystyle y\)-axis and moving right on the \(\displaystyle x\)-axis means addition. 

Moving down the \(\displaystyle y\)-axis and moving left on the \(\displaystyle x-\)axis means subtraction. 

Because we are moving up \(\displaystyle 6\), we can add \(\displaystyle 6\) to our \(\displaystyle y\) coordinate point and because we are moving to the right \(\displaystyle 4\) we can add \(\displaystyle 4\) to our \(\displaystyle x\)coordinate point. 

\(\displaystyle 2+6=8\)

\(\displaystyle 3+4=7\)

\(\displaystyle (7,8)\)

Example Question #299 : Coordinate Geometry

Starting at the coordinate point shown below, if you move up \(\displaystyle 12\) and to the right \(\displaystyle 7\), what is your new point? 


Screen shot 2015 07 30 at 8.51.14 am

Possible Answers:

\(\displaystyle (12,7)\)

\(\displaystyle (10,14)\)

\(\displaystyle (14,10)\)

\(\displaystyle (8,14)\)

\(\displaystyle (7,12)\)

Correct answer:

\(\displaystyle (10,14)\)

Explanation:

The starting point is at \(\displaystyle (3,2)\). When we move up or down we are moving along the \(\displaystyle y\)-axis. When we move to the right or left we are moving along the \(\displaystyle x\)-axis. 

Moving up the \(\displaystyle y\)-axis and moving right on the \(\displaystyle x\)-axis means addition. 

Moving down the \(\displaystyle y\)-axis and moving left on the \(\displaystyle x-\)axis means subtraction. 

Because we are moving up \(\displaystyle 12\), we can add \(\displaystyle 12\) to our \(\displaystyle y\) coordinate point and because we are moving to the right \(\displaystyle 7\) we can add \(\displaystyle 7\) to our \(\displaystyle x\)coordinate point. 

\(\displaystyle 2+12=14\)

\(\displaystyle 3+7=10\)

\(\displaystyle (10,14)\)

Example Question #300 : Coordinate Geometry

Starting at the coordinate point shown below, if you move up \(\displaystyle 11\) and to the right \(\displaystyle 5\), what is your new point? 



Screen shot 2015 07 30 at 8.51.14 am

Possible Answers:

\(\displaystyle (5,2)\)

\(\displaystyle (11,5)\)

\(\displaystyle (2,5)\)

\(\displaystyle (5,11)\)

\(\displaystyle (8,13)\)

Correct answer:

\(\displaystyle (8,13)\)

Explanation:

The starting point is at \(\displaystyle (3,2)\). When we move up or down we are moving along the \(\displaystyle y\)-axis. When we move to the right or left we are moving along the \(\displaystyle x\)-axis. 

Moving up the \(\displaystyle y\)-axis and moving right on the \(\displaystyle x\)-axis means addition. 

Moving down the \(\displaystyle y\)-axis and moving left on the \(\displaystyle x-\)axis means subtraction. 

Because we are moving up \(\displaystyle 11\), we can add \(\displaystyle 11\) to our \(\displaystyle y\) coordinate point and because we are moving to the right \(\displaystyle 5\) we can add \(\displaystyle 5\) to our \(\displaystyle x\)coordinate point. 

\(\displaystyle 2+11=13\)

\(\displaystyle 3+5=8\)

\(\displaystyle (8,13)\)

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