Question

Select the correct answer from each drop-down menu.

Answer 1

Answer:

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

Step-by-step explanation:

We are given that a perpendicular bisector CD is drawn through point C on AB.

The coordinates of point A are (-3,2)

The coordinates pf point B are (7,6).

We have to find the x-intercept of CD

Slope formula:$m=\frac{y_2-y_1}{x_2-x_1}$

By using the formula

Slope of AB=$\frac{6-2}{7+3}=\frac{4}{10}=\frac{2}{5}$

Slope of CD=$-\frac{1}{\frac{2}{5}}=-\frac{5}{2}$

When two lines are perpendicular then slope of one line is equal to negative reciprocal of slope of other line.

Mid point of AB

$x=\frac{-3+7}{2}=2,y=\frac{2+6}{2}=4$

The mid-point of AB is at (2,4)

By using mid-point formula

$x=\frac{x_1+x_2}{2},y=\frac{y_1+y_2}{2}$

The equation of line CD is passing through the point (2,4)  with slope -5/2 is given by

$y-4=-\frac{5}{2}(x-2)$

By using point slope form:$y-y_1=m(x-x_1)$

$y=-\frac{5}{2}(x-2)+4$

Substitute y=0

$-4=-\frac{5}{2}(x-2)$

$x-2=\frac{4\times 2}{5}$

$x-2=\frac{8}{5}$

$x=\frac{8}{5}+2=\frac{8+10}{5}$

$x=\frac{18}{5}$

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

$y=-\frac{5}{2}(x-2)+4$

Substitute x=-52

$y=-\frac{5}{2}(-52-2)+4=139$

Substitute x=-20

$y=-\frac{5}{2}(-20-2)+4=59$

Substitute x=32

$y=-\frac{5}{2}(32-2)+4=-71$

Substitute x=-54

$y=-\frac{5}{2}(-54-2)+4=144$

Hence, point C(32,-71) lies on CD.

Answer 2

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 → 2/5

y(AB) = (2/5).x + b. Calculate b; 6 = (2/5).(7) + b and b = 16/5

y(AB) = (2/5).x +16/5

2. 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 = -1

y(CD) = -(5/2).x + b

We 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 + 9

x intercept when y = 0 → 0= (-5/2)x +9 → x= 18/5So x intercept (18/5,0) 

So the answer is at point B.