The quadrilateral resembles a rectangle since it look like it has two pairs of parallel sides where the adjacent sides are perpendicular. To investigate this, we have to determine the slope of the sides using the Slope Formula.
|c|c|c|c|
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Segment & Points & y_2-y_1/x_2-x_1 & m [0.8em]
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AB & A(- 3,4) B(1,6) & 6- 4/1-( - 3) & 1/2 [0.8em]
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BC & B(1,6) C(5,- 2) & - 2- 6/5- 1 & -2 [0.8em]
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CD & D(1,- 4) C(5,- 2) & - 2-( - 4)/5- 1 & 1/2 [0.8em]
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AD & D(1,- 4) A(- 3,4) & 4-( - 4)/- 3- 1 & -2 [0.8em]We have two pairs of parallel sides which means we know this is a parallelogram.
If this is a rectangle, we also have to make sure that adjacent sides are perpendicular.
&AB ⊥ AD
&DC ⊥ AD
&AB ⊥ BC
&DC ⊥ BC
Since AB ∥ DC and AD ∥ BC, we only have to prove that one set of adjacent sides are perpendicular. Let's investigate if AB ⊥ AD. Since perpendicular lines have slopes whose product equals -1, we can write the following equation.
m_(AB) * m_(AD)? =- 1
By substituting the slopes of AB and AD into the formula we can determine if these sides are perpendicular.
As we can see, AB and AD are perpendicular which means we have enough information to say that the parallelogram is a rectangle.
b To rotate a point, for example A on our quadrilateral, by 90^(∘) clockwise about the origin, draw a segment from A to the origin. Then, use a protractor to measure a 90^(∘) angle clockwise with this segment and draw a second segment of equal length to the first.
If we repeat this procedure for our remaining points, we can draw the rotated rectangle.
Having drawn the rotated polygon we can identify the coordinates of its vertices.
&A'=(4,3)
&B'=(6,- 1)
&C'=(-2,-5)
&D'=(-4,- 1)
