The midpoint of a line segment is (4,2). If one of the endpoints is (-2,3), what is the other endpoint?

(10, 1 )

Step-by-step explanation:

Using the midpoint formula

Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then

midpoint = ( , )

Calculate the coordinates of midpoint and equate each to the given midpoint

(x₁, y₁ ) = - 2, 3), let coordinates of other endpoint = (x, y ) , then

= 4 ( multiply both sides by 2 )

- 2 + x = 8 ( add 2 to both sides )

x = 10

and

= 2 ( multiply both sides by 2 )

3 + y = 4 ( subtract 3 from both sides )

y = 1

coordinates of other endpoint are (10, 1 )

y = 5x + 17

step-by-step explanation:

a perpendicular line will be the opposite reciprocal slope of the given equation.   the slope given is -1/5 so the opposite reciprocal is 5

find b:

7 = 5 (-2) + b

7 = -10 + b

17 = b

write equation

y = 5x + 17