Question

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 A.(3,0) B.(18/5,0) C.(9,0) D.(45/2,0). Point A.(-52,141) B.(-20,57) C.(32,-71) D.(54,-128) lies on CD.

Answer 1

a perpendicular bisector cuts the line in half at 90 degrees
you have the points A and B find the length and also the midpoint D

Answer 2

if x-intercept of CD is the x value when the y value is 0

Answer 3

@sshayer the asker is offline do you need help with this or are you just viewing ?

Answer 4

@bands.17 If you could draw the graph as per coordinates and given details of qualified helper, it would be a great help to teach and help you understand.

Answer 5

A perpendicular BISECTOR cuts the interval AB into two equal sections. Thus the point C where this bisector intersects at right angles must be the midpoint of AB.

So first find the midpoint of AB.


After this we need to find out where the line joining CD cuts the x-axis. This means you will need to find the equation of the line CD. The point-gradient formula is ideal for this.
You will need to calculate the gradient of AB first. CD is perpendicular to AB so its gradient obeys the rule m1 x m2 = -1. Thus the gradient of the perpendicular bisector is the negative reciprocal of AB gradient.

Then sub into the pt gradient formula:
y - y1 = m(x - x1)

Once you found the equation, let y = 0 and solve for x. This will tell you where the x intercept is.
This is shown in the diagram here: