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HiSET: Math : Properties of lines

Study concepts, example questions & explanations for HiSET: Math

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Example Questions

Example Question #1 : Midpoint Of Line Segments

Give the coordinates of the midpoint of the line segment whose endpoints are the intercepts of the line of the equation

2x+ 5y = 40 .

Possible Answers:

(-4, -14)

(-14, -4)

None of the other choices gives the correct response.

(14, 4)

(4, 14)

Correct answer:

(14, 4)

Explanation:

The x-intercept and y-intercept of the line of an equation can be found by substituting 0 for and , respectively, as follows:

x-intercept:

2x+ 5y = 40

Substitute and simplify:

2x+ 5(0)= 40

2x+ 0 = 40

2x= 40

Solve for by dividing by 2 on both sides:

$2x \div 2 = 40 \div 2$

x = 20

The x-intercept of the line is located at (20,0)

The y-intercept can be found by setting x= 0 and solving for in a similar fashion:

2x+ 5y = 40

2 (0)+ 5y = 40

0 + 5y = 40

5y = 40

$5y \div 5 = 40 \div 5$

y = 8

The y-intercept is located at (0,8) .

The midpoint of a line segment, given its endpoints $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ , is located at

$\left ( \frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2} \right )$ ;

substituting accordingly,

$\frac{x_{1}+x_{2}}{2} =\frac{20+8}{2} = \frac{28}{2} = 14$

$\frac{y_{1}+y_{2}}{2} = \frac{ 0+8}{2} = \frac{8}{2} = 4$

The midpoint is located at (14, 4) .

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Example Question #1 : Midpoint Of Line Segments

What is the midpoint of the line segment created by the points (-2,16) and (3,7) ?

Possible Answers:

$(-\frac{5}{2},-\frac{13}{2})$

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

$(\frac{1}{2},\frac{23}{2})$

$(\frac{9}{2},-\frac{17}{2})$

$(\frac{23}{2},\frac{3}{2})$

Correct answer:

$(\frac{1}{2},\frac{23}{2})$

Explanation:

The midpoint of the line segment between two points

$(x_{0},y_{0})$ and $(x_{1},y_{1})$

is given by the formula

$(\frac{x_{0}+x_{1}}{2},\frac{y_{0}+y_{1}}{2})$ .

Thus, since the line segment is generated by

(-2,16) and (3,7)

applying the midpoint formula we have

$(\frac{-2+3}{2},\frac{16+7}{2})= (\frac{1}{2},\frac{23}{2})$

as the midpoint.

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Example Question #1 : Midpoint Of Line Segments

What is the midpoint between A(-12,10) and B(14,-6) ?

Possible Answers:

(-1,2)

(2,1)

(-2,-1)

(1,2)

Correct answer:

(1,2)

Explanation:

Step 1: Recall the midpoint Formula....

$(\dfrac {x_1+x_2}{2},\dfrac {y_1+y_2}{2})$ , where (x_1,y_1) is the first point and (x_2,y_2) is the second point

Step 2: Identify the points and their specific terms...

x_1=-12, y_1=10, x_2=14, y_2=-6

Step 3: Plug in the values into the midpoint formula...

$(\dfrac {-12+14}{2},\dfrac {10-6}{2})$

Simplify...

$(\dfrac {2}{2},\dfrac {4}{2})=(1,2)$

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HiSET: Math : Properties of lines

Study concepts, example questions & explanations for HiSET: Math

All HiSET: Math Resources

Example Questions

Example Question #1 : Midpoint Of Line Segments

Example Question #1 : Midpoint Of Line Segments

Example Question #1 : Midpoint Of Line Segments

All HiSET: Math Resources

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