You can determine midpoint by
x-midpoint = (x₁ + x₂)/2
y-midpoint = (y₁ + y₂)/2
Given from the question
x-midpoint = -6
x₁ = -7
y-midpoint = 5
y₁ = 8
Asked from the question
(x₂, y₂)
Solution
Find x₂, input the value of x₁ and x-midpoint to the formula
(x₁ + x₂)/2 = x-midpoint
(-7 + x₂)/2 = -6
-7 + x₂ = -6 × 2
-7 + x₂ = -12
x₂ = -12 + 7
x₂ = -5
Find y₂, input the value of y₁ and y-midpoint to the formula
(y₁ + y₂)/2 = 5
(8 + y₂)/2 = 5
8 + y₂ = 5 × 2
8 + y₂ = 10
y₂ = 10 - 8
y₂ = 2
Answer
P₂ = (-5,2)
--------------------------------------------------------------
Find Slope
--------------------------------------------------------------
4x + 2y = 2
2y= -4x + 2
y = -4/2 x + 2
y = -2x + 2
Slope = -2
Perpendicular slope = 1/2
--------------------------------------------------------------
Insert slope into the general equation y = mx + c
--------------------------------------------------------------
y = 1/2x + c
--------------------------------------------------------------
Find y-intercept
--------------------------------------------------------------
y = 1/2x + c
at (5,6)
6 = 1/2 (5) + c
6 = 5/2 + c
c = 6 - 5/2
c = 7/2
--------------------------------------------------------------
Insert y-intercept into y = 1/2 x + c
--------------------------------------------------------------
y = 1/2 x + 7/2
2y = x + 7
--------------------------------------------------------------
Answer: 2y = x + 7
--------------------------------------------------------------
The expression that lists all numbers in prime numbers would be A. All numbers here are prime numbers, and is in the simplified form, the remaining choices are not in their simplified forms and can be broken down into smaller numbers that multiply to give their value.
18-2[x+(x-5)]
18-2[2x-5]
18-4x+10
28-4x
-7+x or x-7 <-- Simplified version.
x=7 <-- What x equals.
