ISEE Lower Level Quantitative : Coordinate Geometry

Study concepts, example questions & explanations for ISEE Lower Level Quantitative

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Example Questions

Example Question #1421 : Grade 6

Select the graph that displays the polygon created using the following coordinates:

Possible Answers:

 

Plot 43

 

Plot 42

 

Plot 44

 

Plot 41

Correct answer:

 

Plot 41

Explanation:

When we are given coordinate points, it's important to know the difference between the x-axis and the y-axis, and which order these points are given. The x-axis is the axis that runs left to right and the y-axis is the axis the runs up and down. When coordinate points are written, the x value goes first, followed by the y value .

Knowing this information, we can plot the points and use straight lines to connect them in a counter-clockwise or clockwise direction. The provided coordinate points should create the following graph:

 

Plot 41

Example Question #1422 : Grade 6

Select the graph that displays the polygon created using the following coordinates:

Possible Answers:

 

Plot 46

 

Plot 48

 

Plot 45

 

Plot 47

Correct answer:

 

Plot 45

Explanation:

When we are given coordinate points, it's important to know the difference between the x-axis and the y-axis, and which order these points are given. The x-axis is the axis that runs left to right and the y-axis is the axis the runs up and down. When coordinate points are written, the x value goes first, followed by the y value .

Knowing this information, we can plot the points and use straight lines to connect them in a counter-clockwise or clockwise direction. The provided coordinate points should create the following graph:

 

Plot 45

Example Question #131 : Geometry

Vt_custom_xy_xytriangle_1

Find the area of the above triangle--given that it has a base of  and a height of 

Possible Answers:

 square units

 square units

 square units

 square units

Correct answer:

 square units

Explanation:

To find the area of the right triangle apply the formula: 

Thus, the solution is: 

Example Question #132 : Geometry

Vt_custom_xy_xytriangle2

The above triangle has a base of  and a height of . Find the area. 

Possible Answers:

 square units

 square units

 square units

 square units

Correct answer:

 square units

Explanation:

To find the area of this right triangle apply the formula: 

Thus, the solution is:

Example Question #133 : Geometry

Vt_custom_xy_xytriangle2

The above triangle has a base of  and a height of . Find the length longest side (the hypotenuse). 

Possible Answers:

Correct answer:

Explanation:

In order to find the length of the longest side of the triangle (hypotenuse), apply the formula:

, where  and  are equal to  and , respectively. And,  the hypotenuse.

Thus, the solution is:




Example Question #134 : Geometry

Vt_custom_xy_xytriangle3

The triangle shown above has a base of  and height of . Find the area of the triangle. 

Possible Answers:

 square units

 square units

 square units

 square units

Correct answer:

 square units

Explanation:

To find the area of this triangle apply the formula: 

Thus, the solution is:

Example Question #135 : Geometry

Vt_custom_xy_xytriangle3

At which of the following coordinate points does this triangle intersect with the -axis?

Possible Answers:

Correct answer:

Explanation:

This triangle only intersects with the vertical -axis at one coordinate point: . Keep in mind that the  represents the  value of the coordinate and  represents the  value of the coordinate point. 

Example Question #136 : Geometry

Vt_custom_xy_xytriangle3

The triangle shown above has a base of  and height of . Find the perimeter of the triangle. 

Possible Answers:

Correct answer:

Explanation:

The perimeter of this triangle can be found using the formula: 

Thus, the solution is:



Example Question #137 : Geometry

Vt_custom_xy_xytriangle_4

The above triangle has a height of  and a base with length .  Find the area of the triangle. 

Possible Answers:

 square units

 square units

 square units

 square units

Correct answer:

 square units

Explanation:

In order to find the area of this triangle apply the formula: 

Example Question #138 : Geometry

Vt_custom_xy_xytriangle3

The triangle shown above has a base of  and height of . Find the length of the longest side of the triangle (the hypotenuse). 

Possible Answers:

Correct answer:

Explanation:

In order to find the length of the longest side of the triangle (hypotenuse), apply the formula:

, where  and  are equal to  and , respectively. And,  the hypotenuse. 

Thus, the solution is:




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