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insens350 [35]
3 years ago
7

A perpendicular bisector, CD is drawn through point C on AB. 

Mathematics
2 answers:
trasher [3.6K]3 years ago
6 0

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:

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.

C=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})=(\frac{7-3}{2},\frac{2+6}{2})=(2,4)

The coordinates of C are (2,4).

The slope of line AB is

m_1=\frac{y_2-y_1}{x_2-x_1}=\frac{6-2}{7-(-3)}=\frac{4}{10}=\frac{2}{5}

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

m_2=-\frac{5}{2}

The point slope form of a line is

y-y_1=m(x-x_1)

The slope of line CD is -\frac{5}{2} and the line passing through the point (2,4), the equation of line CD is

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

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

y=-\frac{5}{2}x+9       .... (1)

The equation of CD is y=-\frac{5}{2}x+9.

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

0=-\frac{5}{2}x+9

\frac{5}{2}x=9

x=\frac{18}{5}

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

Put x=-52 in equation (1).

y=-\frac{5}{2}(-52)+9=139

Put x=-20 in equation (1).

y=-\frac{5}{2}(-20)+9=59

Put x=32 in equation (1).

y=-\frac{5}{2}(32)+9=-71

Put x=-54 in equation (1).

y=-\frac{5}{2}(-54)+9=144

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

STALIN [3.7K]3 years ago
3 0

<u>Answer</u>

B(18/5,0)


<u>Explanation</u>

First we find the coordinates of C;

C (x, y) = [(-3+7)/2, (2+6)/2]

           = (2, 4)

Find the equation of CD.

slope = (6-2)/(7--3)

         = 4/10  = 2/5

slope of CD = -5/2

-5/2 = (y - 4)/(x - 2)

-5/2(x - 2) = y - 4

(-5/2) x + 5 = y - 4

y = (-5/2)x + 9

For the x-intercept y = 0

∴ y = (-5/2)x + 9  

 0 = (-5/2)x + 9  

5/2 x = 9

x = 2/5 × 9

  = 18/5

x-intercept  = (18/5, 0)


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