Properties of lines - HiSet: High School Equivalency Test: Math

Card 0 of 3

Question

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

.

Answer

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:

Substitute and simplify:

Solve for by dividing by 2 on both sides:

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

The x-intercept of the line is located at

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

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

The y-intercept is located at .

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 .

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Question

What is the midpoint of the line segment created by the points and ?

Answer

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

and

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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Question

What is the midpoint between and ?

Answer

Step 1: Recall the midpoint Formula....

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

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

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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