MATH SOLVE

4 months ago

Q:
# The endpoints of AB are A(2, 3) and B(8, 1). The perpendicular bisector of AB is CD, and point C lies on AB. The length of CD is (root of 10) units.The coordinates of point C are (-6, 2) (5, 2) (6, -2) (10, 4) . The slope of is -3 -1/3 1/3 3 . The possible coordinates of point D are (4, 5) (5, 5) (6, 5) (8, 3) and (2, 1) (4, -1) (5, -1) (6, -1) .Please pick 1 answer for all the questions

Accepted Solution

A:

Comment

If C lies on AB Then it must be the midpoint of AB because CD is the Perpendicular Bisector of AB

Midpoint

A(2,3) B(8,1)

Midpoint formula = (x1 + x2)/2 + (y1 + y2)/2

Midpoint = (2 + 8)/2 + (3 + 1) / 2

Midpoint = 10/2 + 4/2

Midpoint = (5,2) <<<<< answer

Slope AB

slope = (y2 - y1)/(x2 - x1)

slope = (3 - 1) / (2 - 8)

slope = 2/-6 = -1/3

Slope CD

CD_slope * AB_slope = - 1

CD_slope * -1/3 = -1 multiply both sides by - 3

CD_slope * 1 = - 1 * -3

CD_slope = 3 <<<<< Slope CD Answer

Equation CD

Given the midpoint of AB which is C( and the slope of CD

y = 3x + b

2 = 3*5 + b

b = - 13

Equation y = 3x - 13

Using Distance to get D

d^2 = (x1 - x2)^2 + (y2 - y1)'^2

d^2 = (x2 - 5)^2 + (y2 - 2)^2

y2 = 3*x2 - 13

10 = x2^2 - 10x2 + 25 + (3x2 - 13 - 2)^2

10 = x2^2 - 10x2 + 25 + (3x2 - 15)^2

10 = x1^2 - 10x2 + 25 + 9x^2 - 90x2 + 225

10 = 10x2^2 - 100x2 +250

0 = 10x2^2 - 100x2 + 240 Divide through by 10

0 = x2^2 - 10x^2 + 24

0 = (x2 - 6)(x2 - 4)

x2 = 6 or

x2 = 4

Using y2 = 3x - 13

for x2 = 4

then y2 = 3(4) - 13

y2 = - 1

for x2 = 6

y2 = 3*6 - 13

y2 = 5

Possible Answers for D

D = (4,-1)

D = (6,5)

I've included a graph to show a graphical solution.

Please note in a week's time, if no one else answers, you can award a Brainly. This question took over an hour. If someone else answers, please choose one of us.

If C lies on AB Then it must be the midpoint of AB because CD is the Perpendicular Bisector of AB

Midpoint

A(2,3) B(8,1)

Midpoint formula = (x1 + x2)/2 + (y1 + y2)/2

Midpoint = (2 + 8)/2 + (3 + 1) / 2

Midpoint = 10/2 + 4/2

Midpoint = (5,2) <<<<< answer

Slope AB

slope = (y2 - y1)/(x2 - x1)

slope = (3 - 1) / (2 - 8)

slope = 2/-6 = -1/3

Slope CD

CD_slope * AB_slope = - 1

CD_slope * -1/3 = -1 multiply both sides by - 3

CD_slope * 1 = - 1 * -3

CD_slope = 3 <<<<< Slope CD Answer

Equation CD

Given the midpoint of AB which is C( and the slope of CD

y = 3x + b

2 = 3*5 + b

b = - 13

Equation y = 3x - 13

Using Distance to get D

d^2 = (x1 - x2)^2 + (y2 - y1)'^2

d^2 = (x2 - 5)^2 + (y2 - 2)^2

y2 = 3*x2 - 13

10 = x2^2 - 10x2 + 25 + (3x2 - 13 - 2)^2

10 = x2^2 - 10x2 + 25 + (3x2 - 15)^2

10 = x1^2 - 10x2 + 25 + 9x^2 - 90x2 + 225

10 = 10x2^2 - 100x2 +250

0 = 10x2^2 - 100x2 + 240 Divide through by 10

0 = x2^2 - 10x^2 + 24

0 = (x2 - 6)(x2 - 4)

x2 = 6 or

x2 = 4

Using y2 = 3x - 13

for x2 = 4

then y2 = 3(4) - 13

y2 = - 1

for x2 = 6

y2 = 3*6 - 13

y2 = 5

Possible Answers for D

D = (4,-1)

D = (6,5)

I've included a graph to show a graphical solution.

Please note in a week's time, if no one else answers, you can award a Brainly. This question took over an hour. If someone else answers, please choose one of us.