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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.

User Nruth
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2 Answers

5 votes

Answer:

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

Explanation:

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User AMK
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3 votes

Answer:

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

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=((x_1+x_2)/(2),(y_1+y_2)/(2))=((7-3)/(2),(2+6)/(2))=(2,4)

The coordinates of C are (2,4).

The slope of line AB is


m_1=(y_2-y_1)/(x_2-x_1)=(6-2)/(7-(-3))=(4)/(10)=(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=-(5)/(2)

The point slope form of a line is


y-y_1=m(x-x_1)

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


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


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


y=-(5)/(2)x+9 .... (1)

The equation of CD is
y=-(5)/(2)x+9.

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


0=-(5)/(2)x+9


(5)/(2)x=9


x=(18)/(5)

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

Put x=-52 in equation (1).


y=-(5)/(2)(-52)+9=139

Put x=-20 in equation (1).


y=-(5)/(2)(-20)+9=59

Put x=32 in equation (1).


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

Put x=-54 in equation (1).


y=-(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.

User Daniel Eberl
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7.1k points

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