Select the correct answer from each drop-down menu.A perpendicular bisector, , is drawn through point C on .If the coordinates of point A are (-3, 2) and the coordinates of point B are (7, 6), the x-intercept of is . Point lies on .
Accepted Solution
A:
Answer:The following steps are needed:1. Find the function of AB with A(-3,2) and B(7,6)y(AB) = mx + b. Calculate m = (y₂-y₁)/(x₂-x₁) = (6-2)/(7+3) = 4/10 → 2/5y(AB) = (2/5).x + b. Calculate b; 6 = (2/5).(7) + b and b = 16/5y(AB) = (2/5).x +16/52. calculate the function y(CD) = mx + bWe know already m = -5/2, since CD is perpendicular to AB and hence the product of their slopes = -1y(CD) = -(5/2).x + bWe also know that y(CD) passes in the middle of AB, then let's calculate the coordinate of C, the midpoint of AB:x=(x₁+x₂)/2 and y=(y₁+y₂)/2)x= (-3+7)/2 and y=(2+6)/2x= 2 and y=4y(CD) = (-5/2).x +b4 = (-5/2).(2)+b and b = 9y(CD) =(-5/2)x + 9x intercept when y = 0 → 0= (-5/2)x +9 → x= 18/5So x intercept (18/5,0) So the answer is at point B.