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Intermediate Geometry : Lines

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Example Question #71 : Lines

Find the length of a line with endpoints at (10, 2) and (5, -6) .

Possible Answers:

$\sqrt{89}$

$\sqrt{91}$

$\sqrt{85}$

$\sqrt{87}$

Correct answer:

$\sqrt{89}$

Explanation:

Recall the distance formula for a line with two endpoints $(x_1, y_1)\text{ and }(x_2, y_2)$ :

$\text{distance}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Plug in the given points to find the length of the line:

$\text{distance}=\sqrt{(5-10)^2+(-6-2)^2}=\sqrt{89}$

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Example Question #17 : Distance Formula

A line segment on the coordinate plane has its endpoints at (3.8, -1.7) and (9.2, 5.5) .

Give the length of the segment to the nearest whole tenth.

Possible Answers:

6.6

15.2

13.5

9.0

14.8

Correct answer:

9.0

Explanation:

The distance between endpoints $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ on the coordinate plane can be calculated using the distance formula

$d = \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

Set $x_{1}= 3.8, y_{1} =-1.7,x_{2} =9.2, y_{2}= 5.5$ , and evaluate:

$d = \sqrt{(9.2-3.8)^{2}+[5.5 -(-1.7)]^{2}}$

$= \sqrt{5.4 ^{2}+7.2^{2}}$

$= \sqrt{29.16+51.84}$

$= \sqrt{81}$

= 9 ,

the correct length.

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Example Question #1 : How To Find Out If A Point Is On A Line With An Equation

A line passes through both the origin and the point (12,5) . Which of the following points are NOT on the line?

Possible Answers:

(-3,-1.25)

(6,2.5)

(14.4,6)

(20.4,8.5)

(15.6,8)

Correct answer:

(15.6,8)

Explanation:

Because the line passes through the origin, all of the points on the line will have an x:y ratio of 12:5 . Only $\left ( 15.6,8 \right )$ does not meet this requirement.

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Example Question #1 : Other Lines

Which of the following points does NOT lie on the graph of y=x^2-3x+7

Possible Answers:

(2,5)

(3,7)

(4,12)

(1,5)

(5,17)

Correct answer:

(4,12)

Explanation:

To find if a point lies on a graph or not, simply plug the x and y values into your equation and see if it holds true. Plugging our x values into the equation y=x^2-3x+7 gives us the following:

x=1: y=(1)^2-3(1)+7=5

x=2: y=(2)^2-3(2)+7=5

x=3: y=(3)^2-3(3)+7=7

x=4: y=(4)^2-3(4)+7=11 and

x=5: y=(5)^2-3(5)+7=17

So our points are (1,5), (2,5), (3,7), (4,11), and (5,17) . This makes (4,12) the only point that does not lie on our graph.

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Example Question #1 : How To Find Out If A Point Is On A Line With An Equation

Which of the following points exists on the line 2x-2y=1 ?

Possible Answers:

$( 1,\frac{1}{2})$

$(0,\frac{1}{2})$

$( 1,-\frac{1}{2})$

(0,1)

(1,0)

Correct answer:

$( 1,\frac{1}{2})$

Explanation:

Substitute each answer choice into the equation in question, 2x-2y=1 , in order to test if the equation is valid at the given point

Only $( 1,\frac{1}{2})$ will satisfy the equation on both the left and right side.

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Example Question #4 : How To Find Out If A Point Is On A Line With An Equation

Which of the following points exist on the line x=1 ?

Possible Answers:

(1,20)

(-1,0)

(20,1)

(0,1)

(0,-1)

Correct answer:

(1,20)

Explanation:

The line x=1 is a vertical line. This means that any point with an -value of will exist on the line.

The only possible point with an -value of is (1,20) .

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Example Question #5 : How To Find Out If A Point Is On A Line With An Equation

Which point will exist on the line y=-1 ?

Possible Answers:

(-1,1)

(1000,-1)

(-1,0)

(-1,1000)

(1000,1000)

Correct answer:

(1000,-1)

Explanation:

The line y=-1 is a horizontal line with points all -values equal to .

The only possible answer with a -value of is (1000,-1) .

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Example Question #6 : How To Find Out If A Point Is On A Line With An Equation

Which point is on the line y = 2x - 4 ?

Possible Answers:

(2,0)

$(\frac{1}{2}, -3 )$

(1,-2)

$(-\frac{1}{2}, 5)$

(-1,-6)

Correct answer:

$(-\frac{1}{2}, 5)$

Explanation:

A point is on a line if, plugged in, it creates a true mathematical equation.

For example, (1,-2) is definitely on the line because when you plug it in, it creates a true equation:

y = 2x - 4 plug in the and values

-2 = 2(1) - 4 multiply

-2 = 2-4

-2 = -2 this is true, so that point is on the line

The point that does not work is $(-\frac{1}{2}, 5)$ :

$5 = 2(-\frac{1}{2 }) -4$ multiply

5 = -1 - 4 subtract

$5 \neq -5$

Since this is not true, the point is NOT on the line.

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Example Question #1 : Other Lines

Which point is NOT on the line $y = \frac{2}{3} x - 5$ ?

Possible Answers:

(6, 1)

(-3, -7)

(3,-3)

(6, -1 )

(6,-9)

Correct answer:

(6, 1)

Explanation:

A point is on a line if, plugged in, it creates a true mathematical equation.

For example, (3,-3) is definitely on the line because when you plug it in, it creates a true equation:

$y = \frac{2}{3}x - 5$ plug in the and values

$-3 =\frac{2}{3}(3) - 5$ multiply

-3 = 2-5

-3= -3 this is true, so that point is on the line

The point that does not work is (6, 1) :

$1 = \frac{2}{3}(6) -5$ multiply

1 = 4- 5 subtract

$1 \neq -1$

Since this is not true, the point is NOT on the line.

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Example Question #8 : How To Find Out If A Point Is On A Line With An Equation

Which point is NOT on the line $y = \frac{1}{4} x + 3$ ?

Possible Answers:

(-4,2)

(-4,4)

(-8, 1)

(4,4)

(8,5)

Correct answer:

(-4,4)

Explanation:

A point is on a line if, plugged in, it creates a true mathematical equation.

For example, (-4, 2) is definitely on the line because when you plug it in, it creates a true equation:

$y = \frac{1}{4}x +3$ plug in the and values

$2 = \frac{1}{4}(-4) +3$ multiply

2 = -1+3

2 =2 this is true, so that point is on the line

The point that does not work is (-4, 4) :

$4 =\frac{1}{4} (-4)+3$ multiply

4 = -1 +3 subtract

$4 \neq -2$

Since this is not true, the point is NOT on the line.

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Intermediate Geometry : Lines

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #71 : Lines

Example Question #17 : Distance Formula

Example Question #1 : How To Find Out If A Point Is On A Line With An Equation

Example Question #1 : Other Lines

Example Question #1 : How To Find Out If A Point Is On A Line With An Equation

Example Question #4 : How To Find Out If A Point Is On A Line With An Equation

Example Question #5 : How To Find Out If A Point Is On A Line With An Equation

Example Question #6 : How To Find Out If A Point Is On A Line With An Equation

Example Question #1 : Other Lines

Example Question #8 : How To Find Out If A Point Is On A Line With An Equation

All Intermediate Geometry Resources

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