SAT

What is the midpoint of line segment CD?

(1,0)
(1,–3)
(2,0)
(2,–1)
(4,6)

Solution

The coordinates of point C are (–3,6) and the coordinates of point D are (5,–6). The midpoint of a line is equal to the average of the x values of the endpoints and the average of the y values of the endpoints:\(\left ( \frac{-3+5}{2},\frac{6+(-6)}{2} \right )=\left ( \frac{2}{2},-\frac{0}{2} \right )= (1,0)\).

What is the midpoint of line segment AB?

(1.5,–1)
(0,2)
(4,0)
(2,–1)
(4,–2)

Solution

The coordinates of point A are (–5,–4) and the coordinates of point B are (9,2). The midpoint of a line is equal to the average of the x values of the endpoints and the average of the y values of the endpoints:\(\left ( \frac{-5+9}{2},\frac{-4+2}{2} \right )=\left ( \frac{4}{2},-\frac{2}{2} \right )= (2,-1)\)

The endpoints of a line segment are (0,–4) and (0,4). What is the midpoint of this line?

(0,0)
(0,–2)
(0,2)
(–4,4)
This line has no midpoint.

Solution

The midpoint of a line is equal to the average of the x values of the endpoints and the average of the y values of the endpoints:\(\left ( \frac{0+0}{2},\frac{-4+2}{2} \right )=\left ( \frac{0}{2},-\frac{0}{2} \right )= (0,0)\).

What is the midpoint of a line segment with endpoints at (6,–4) and (15,8)?

(9,4)
(9,12)
(10.5,2)
(12,2)
(12,9)

Solution

The midpoint of a line segment is equal to the average of the x values of the endpoints and the average of the y values of the endpoints:\(\left ( \frac{6+16}{2},\frac{-4+8}{2} \right )=\left ( \frac{21}{2},\frac{4}{2} \right )= (10,5,2)\).

What is the midpoint of a line segment with endpoints at (0,–8) and (–8,0)?

(–8,–8)
(–4,–4)
(–1,–1)
(4,4)
(8,8)

Solution

The midpoint of a line segment is equal to the average of the x values of the endpoints and the average of the y values of the endpoints:\(\left ( \frac{0+(-8)}{2},\frac{-8+0}{2} \right )=\left ( \frac{21}{2},\frac{4}{2} \right )= (–4,–4)\).

What is the slope of line segment CD?

¹⁄₅
1
3
5
15

Solution

The coordinates of point A are (–5,1) and the coordinates of point B are (5,–4). The slope of a line is the difference between the y values of two points divided by the difference between the x values of those two points:\(\frac{-4-1}{5-(-5)}=\frac{-5}{10}=-\frac{1}{2}\).

What is the slope of line segment AB?

–¹⁄₂
–1
–2
–5
–10

Solution

The coordinates of point A are (–5,1) and the coordinates of point B are (5,–4). The slope of a line is the difference between the y values of two points divided by the difference between the x values of those two points: \(\frac{-4-1}{5-(-5)}=\frac{-5}{10}=-\frac{1}{2}\)

What is the slope of a line segment with endpoints at (–1,2) and (1,10)?

–4
–¹⁄₄
¹⁄₄
4
This line has no slope.

Solution

The slope of a line is the difference between the y values of two points divided by the difference between the x values of those two points: \(\frac{10-2}{1-(-1)}=\frac{8}{2}=4\).

The endpoints of a line segment are (5,–5) and (–5,–5). What is the slope of this line?

–10
–5
Zero
5
This line has no slope.

Solution

The slope of a line is the difference between the y values of two points divided by the difference between the x values of those two points: \(\frac{-5-(-5)}{-5-5}=\frac{0}{-10}=0\).

The endpoints of a line segment are (–3,6) and (7,4). What is the slope of this line?

–5
–¹⁄₅
¹⁄₅
5
10

Solution

The slope of a line is the difference between the y values of two points divided by the difference between the x values of those two points:\(\frac{4-6}{7-(-3)}=\frac{-2}{10}=-\frac{1}{5}\).

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