Answer:
The x-intercept of CD is B(18/5,0). The point C(32,-71) lies on the line CD.
Step-by-step explanation:
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.
Given :
CD is perpendicular bisector of AB.
The coordinates of point A are (-3, 2) and the coordinates of point B are (7, 6).
C is the midpoint of AB.
The coordinates of C are (2,4).
Line AB has a slope of:
The product of slopes of two perpendicular lines is -1. Since the line CD is perpendicular to AB, therefore the slope of CD :
The point slope form of a line is given by:
The slope of line CD is and the line passing through the point (2,4), the equation of line CD can be written as:
The equation of CD is
In order to find the x-intercept, put y=0.
Therefore the x-intercept of CD is B(18/5,0).
Put x=-52 in eq(1).
Put x=-20 in eq(1).
Put x=32 in eq(1)
Put x=-54 in eq1).
Thus, only point (32,-71) satisfies the equation of CD. Therefore the point C(32,-71) lies on the line CD.