Question

Please help me figure this out because everything I've tried doesn't work. I NEED TO FINISH THIS TO GRADUATE PLEASE PLEASE PLEASE HELP ME!

A perpendicular bisector, CD , is drawn through point C on AB.
If the coordinates of point A are (-3, 2) and the coordinates of point B are (7, 6), the x-intercept of CD is ____ . Point ___ lies on CD.

Part 1 options
(3,0)
(18/5,0)
(9,0)
(45/2,0)

Part 2 options
(-52,141)
(-20,57)
(32,-71)
(54,-128)

Answer 1

1. (18/5,0)
First let us find the equation of AB. It should be in the form of y=mx + b
From the given coordinates, you can get m, x, and b.

m= y2-y1 divided by x2 - x1
m=(6-2)/(7- -3)= 4/10 or 2/5
m= 2/5

b is your y intercept
To get it, use 1 coordinate either from point A or B.
Let point A be the coordinates
y=mx + b
-3= 2/5(2) + b
b= - 3- 4/5
b= 16/5


Now we will find the equation of CD,
y=mx + b
y= (-5/2)x + b
Then get the coordinates of point C through midpoint equation,
(x1+x2) /2, (y1+y2) /2
(-3+7)/2, (2+6)/2
=C(2,4)
We will use this coordinates to find b,
y=mx+b
4=(-5/2)2+b
4+5=b
b=9
If we are finding the x intercept, y value should be 0.
0=(-5/2)x+9
0-9(2)/-5=x
x= 18/5
The x intercept of CD is (18/5,0)

2. The answer is (54,-128)