Question

On a coordinate plane, 4 lines are shown. Line A B goes through (negative 4, negative 2) and (4, 2). Line C D goes through (negative 4, 0) and (4, negative 4). Line F G goes through (negative 3, negative 3) and (0, 3). Line H J goes through (negative 1, 3) and (1, negative 1). Which line is perpendicular to a line that has a slope of One-half? line AB line CD line FG line HJ

Answer 1

Answer:

The line is HJ

Step-by-step explanation:

we know that

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

step 1

Find the slope line AB

we have

A(-4,-2),B(4,2)

substitute the values in the formula

$m=\frac{2+2}{4+4}$

$m=\frac{4}{8}$

$m_A_B=\frac{1}{2}$

step 2

Find the slope line CD

we have

C(-4,0),D(4,-4)

substitute the values in the formula

$m=\frac{-4-0}{4+4}$

$m=\frac{-4}{8}$

$m_C_D=-\frac{1}{2}$

step 3

Find the slope line FG

we have

F(-3,-3),G(0,3)

substitute the values in the formula

$m=\frac{3+3}{0+3}$

$m=\frac{6}{3}$

$m_F_G=2$

step 4

Find the slope line HJ

we have

H(-1,3),J(1,-1)

substitute the values in the formula

$m=\frac{-1-3}{1+1}$

$m=\frac{-4}{2}$

$m_H_J=-2$

step 5

Compare the slopes

we have

$m_A_B=\frac{1}{2}$

$m_C_D=-\frac{1}{2}$

$m_F_G=2$

$m_H_J=-2$

we know that

If two lines are perpendicular, then their slopes are opposite reciprocal

so

The slope of a line perpendicular to a line that has a slope of One-half must be negative 2

therefore

The line is HJ

Answer 2

Answer:

D or line HJ

Step-by-step explanation: