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# analytic geometry

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(a) Find the coordinates of the midpoint of AB with endpoints A(-2,1) and B(5,4).

(b) Find the line that is perpendicular to the segment that passes through the midpoint (the perpendicular bisector).

Mar 11, 2021

#1
+928
0

Hi Guest!

A

Midpoint is just the average.

The x coordinates are -2 and 5, so the average is 1.5.

The y coordinates are 1 and 4, so the average is 2.5.

So the midpoint is (1.5, 2.5).

B

The perpendicular segment has a negative recipical slope.

To graph AB, the slope is (4-1)(5--2) = 3/7.

So the new slope is -7/3.

y = -7/3x + b

To find b, we can just plug in the points 1.5, 2.5.

2.5 = -7/3(1.5) + b

2.5 = -3.5 + b

b = 7

y = -7/3x + 7

I hope this helped. :))

=^._.^=

Mar 11, 2021

#1
+928
0

Hi Guest!

A

Midpoint is just the average.

The x coordinates are -2 and 5, so the average is 1.5.

The y coordinates are 1 and 4, so the average is 2.5.

So the midpoint is (1.5, 2.5).

B

The perpendicular segment has a negative recipical slope.

To graph AB, the slope is (4-1)(5--2) = 3/7.

So the new slope is -7/3.

y = -7/3x + b

To find b, we can just plug in the points 1.5, 2.5.

2.5 = -7/3(1.5) + b

2.5 = -3.5 + b

b = 7

y = -7/3x + 7

I hope this helped. :))

=^._.^=

catmg Mar 11, 2021