Arectangle 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

B.

Step-by-step 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

where and are points on the line.

Thus

Simplifying fraction.

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

Using point (-5,4)

Using distribution

Adding 4 to both sides.

Taking LCD to add fraction.

Equation of side J.

Finding equation of side L.

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

Slope of line

where and are points on the line.

Thus

Simplifying fraction.

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

Using point (0,-10)

Subtracting both sides by 10.

Equation of side L.

The equation of side perpendicular to side K is represented by

(2x + 16) + (x) = 180

step-by-step explanation:

given,

abcd is a quadrilateral inscribed in a circle

angle a is labeled x plus 16, (x + 16)

angle b is labeled x degrees, (x)

angle c is labeled 6x minus 4, (6x – 4)

angle d is labeled 2x plus 16, (2x + 16)

what equation can be used to solve for angle b?

we know that the sum of the opposite angles of a simple quadrilateral inscribed in a circle is 180 degrees.

angle b is opposite angle d

therefore, angle b + angle d = 180

(x) + (2x + 16) = 180 

same as (2x + 16) + (x) = 180