Question

A rectangle is graphed on the coordinate grid. Which represents the equation of a side that is perpendicular to side k

A. Y=1/4x-10
B. Y=-1/4x-10
C. Y=4x+24
D. Y=4x-10

Answer 1

B.
`y=-(1)/(4)x-10`

Explanation:

Given rectangle with sides J,K,L and M.

We need to find equation of sides that are perpendicular to side K.

For a rectangle adjacent sides are perpendicular to each other.

For side K, the adjacent sides are J and L. Hence, sides J and L are perpendicular to side L.

Finding equation of side J.

Points: (-5,4) and (3,2)

Slope of line
`m=(y_2-y_1)/(x_2-x_1)`

where
`(x_1,y_1)` and
`(x_2,y_2)` are points on the line.

Thus
`m=(2-4)/(3-(-5))`

`m=(2-4)/(3+5)`

`m=(-2)/(8)`

Simplifying fraction.

`m=-(1)/(4)`

Using point-slope equation to find equation of the line.

`(y-y_1)=m(x-x_1)`

Using point (-5,4)

`(y-4)=-(1)/(4)(x-(-5))`

`(y-4)=\-frac{1}{4}(x+5))`

Using distribution

`(y-4)=-(1)/(4)x-(5)/(4)`

Adding 4 to both sides.

`y-4+4=-(1)/(4)x-(5)/(4)+4`

Taking LCD to add fraction.

`y=-(1)/(4)x-(5)/(4)+(16)/(4)`

Equation of side J.

`y=-(1)/(4)x-(11)/(4)`

Finding equation of side L.

Points: (-8,-8) and (0,-10)

Slope of line
`m=(y_2-y_1)/(x_2-x_1)`

where
`(x_1,y_1)` and
`(x_2,y_2)` are points on the line.

Thus
`m=(-10-(-8))/(0-(-8))`

`m=(-10+8)/(0+8)`

`m=(-2)/(8)`

Simplifying fraction.

`m=-(1)/(4)`

Using point-slope equation to find equation of the line.

`(y-y_1)=m(x-x_1)`

Using point (0,-10)

`(y-(-10))=-(1)/(4)(x-0)`

`y+10=-(1)/(4)x`

Subtracting both sides by 10.

`y+10-10=-(1)/(4)x-10`

Equation of side L.

`y=-(1)/(4)x-10`

The equation of side perpendicular to side K is represented by

`y=-(1)/(4)x-10`