MATH SOLVE

4 months ago

Q:
# 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(-52,117) B(-20,57) C(32,-71) D(-54,-128) ] lies on CD

Accepted Solution

A:

The slope of AB is (6 - 2) / (7 + 3) = 2/5. Therefore, the slope of the perpendicular bisector is -5/2. The midpoint of AB is [(-3 + 7)/2, (2 + 6)/2] = (2, 4). Therefore the equation of CD is:

y = (-5/2)x + b, and substituting (2, 4):

4 = -5 + b

b = 9

y = (-5/2)x + 9

The x-intercept is 0 = (-5/2)x + 9

x = 18/5, so the x-intercept is (18/5, 0), which is choice B.

Substituting the four given points reveals that only the 3rd choice: C(32, -71) fits the equation of the line, as:

-71 = (-5/2)(32) + 9

-71 = -80 + 9

-71 = -71 is true, while all the other 3 points don't fit.

y = (-5/2)x + b, and substituting (2, 4):

4 = -5 + b

b = 9

y = (-5/2)x + 9

The x-intercept is 0 = (-5/2)x + 9

x = 18/5, so the x-intercept is (18/5, 0), which is choice B.

Substituting the four given points reveals that only the 3rd choice: C(32, -71) fits the equation of the line, as:

-71 = (-5/2)(32) + 9

-71 = -80 + 9

-71 = -71 is true, while all the other 3 points don't fit.