Aperpendicular 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(-52,117) b(-20,57) c(32,-71) d(-54,-128) ] lies on cd.

The x-intercept of CD is B(18/5,0). The point C(32,-71) lies on the line CD.

Step-by-step explanation:

Given information: CD is perpendicular bisector of AB.

The coordinates of point A are (-3, 2) and the coordinates of point B are (7, 6).

Midpoint of AB is C.

The coordinates of C are (2,4).

The slope of line AB is

The product of slopes of two perpendicular lines is -1. Since the line CD is perpendicular to AB, therefore the slope of CD is

The point slope form of a line is

The slope of line CD is and the line passing through the point (2,4), the equation of line CD is

      .... (1)

The equation of CD is .

Put y=0, to find the x-intercept.

Therefore the x-intercept of CD is B(18/5,0).

Put x=-52 in equation (1).

Put x=-20 in equation (1).

Put x=32 in equation (1).

Put x=-54 in equation (1).

Only point (32,-71) satisfies the equation of CD. Therefore the point C(32,-71) lies on the line CD.

a: 1/6, j: 1/4

step-by-step explanation: you are welcome