Question

Please help 40 points!!

Answer 1

The midpoint is (-1,1)

Equation: y = -x -2

Explanation:

Midpoint:

(
`(-5+3)/(2)`,
`(-5 + 3 )/(2)`) You are taking the averages of the x values and the y values.

(
`(-2)/(2)`,
`(-2)/(2)`)

(-1,-1)

Equation:

The slope of the 2 points given is

`(3 - -5)/(3- - 5)` =
`(8)/(8)` = 1 The slope is the change of y over the change in x. Points are given in the form (x,y) So, I subtracted the y values on top and the x values on the bottom of the fraction.

The equation that is created is perpendicular to the original line, so it slope is the negative reciprocal.

1 as a fraction is
`(1)/(1)`. negative reciprocal means turn the fraction upside down and take the opposite value. If I flip
`(1)/(1)` upside down, I get the same fraction which is equal to 1. Now I will take the opposite sign. Since it is positive, the new slope will be negative

slope -1

x = -1

y = -1

I am using the point that will be on the new line. This is the midpoint that we just found (-1,-1) I am going to plug in the number that I know and solve for b or the y=intercept.

y = mx + b

- 1 = -1(-1) + b

-1 = 1 + b Subtract 1 from both sides of the equation

-2 = b

y = mx + b

y = -1x -2

or

y = -x -2