Question

Help please :)
Prove or disprove that the quadrilateral defined by the points A(6,2), B(3,4), C(1,1), D(4,-1) is a rectangle.

Answer 1

@Directrix

Answer 2

Slope(m)=-0.667 This is the answer to the one u told me to find using the calculator.

Answer 3

@Directrix

Answer 4

Consider that to be -2/3 as the slope for segment AB.

Answer 5

What is the slope for segment BC? B(3,4), C(1,1)

http://calculator.tutorvista.com/slope-calculator.html

Answer 6

Slope(m)=
1.5

Answer 7

Segment AB has slope -2/3.
Segment BC has slope 3/2.

-2/3 * 3/2 = -1.

If the product of the slopes of two lines is -1, then the lines are perpendicular.

So, Segment AB is perpendicular to segment BC.

Answer 8

What is the slope for segment CD?

C(1,1), D(4,-1)

Answer 9

Slope(m)=-0.667

Answer 10

Slope of CD = =2/3


What is the slope of segment DA?

D(4,-1) A(6,2)

Answer 11

Slope(m)=
1.5

Answer 12

Slope of CD =-2/3
Slope of DA = 3/2

Segment CD is perpendicular to Segment DA.
There is a right angle at vertex D of the quadrilateral.

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Segment AB has slope -2/3.
Segment BC has slope 3/2.
-2/3 * 3/2 = -1.

If the product of the slopes of two lines is -1, then the lines are perpendicular.
So, Segment AB is perpendicular to segment BC.

There is a right angle at vertex B of the quadrilateral.
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Segment DA is perpendicular to segment AB because the product of the slopes of the segments is -1. 3/2 * -2/3 = -1.

There is a right angle at A in the quadrilateral.

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Segment BC is perpendicular to segment CD because the product of the slopes is -1.

3/2 * -2/3 = -1

There is a right angle at vertex C of the quadrilateral.

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The quadrilateral has 4 right angles which means that the quadrilateral is a rectangle.

Answer 13

That the answer?