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

D or line HJ

Explanation:

Answer 2

The line is HJ

Explanation:

we know that

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

`m=(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=(2+2)/(4+4)`

`m=(4)/(8)`

`m_A_B=(1)/(2)`

step 2

Find the slope line CD

we have

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

substitute the values in the formula

`m=(-4-0)/(4+4)`

`m=(-4)/(8)`

`m_C_D=-(1)/(2)`

step 3

Find the slope line FG

we have

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

substitute the values in the formula

`m=(3+3)/(0+3)`

`m=(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=(-1-3)/(1+1)`

`m=(-4)/(2)`

`m_H_J=-2`

step 5

Compare the slopes

we have

`m_A_B=(1)/(2)`

`m_C_D=-(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