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### Course: High school geometry>Unit 6

Lesson 4: Parallel & perpendicular lines on the coordinate plane

# Classifying figures with coordinates

Use coordinates to determine the slopes of sides of a figure in order to classify it. Created by Sal Khan.

## Want to join the conversation?

• How exactly would taking the opposite reciprocal confirm that it is a 90 degree angle?
• how am I supposed to find the answer when he uses a graph every time, but none of the problems give you a graph to solve it on?
• Using the equation that Sal used to find if AB and BC were perpendicular, and knowing that the shape is a parallelogram, this is solvable.
Hope this helps.
• Can we use the distance formula for diagonals BD and AC and check if they are equal? If BD=AC then it's a rectangle, otherwise not
(1 vote)
• Actually, knowing that BD = AC alone does not guarantee that ABCD is a rectangle. We would need the additional condition that ABCD is a parallelogram.

For example, consider A(-2, 0), B(0, 2), C(1, 0), D(0, -1) in clockwise order.
Then BD = AC = 3. However, ABCD is not a rectangle because the slopes of BC and CD (which are -2 and 1) are not negative reciprocals (making C not a right angle).

Have a blessed, wonderful day!
• At the start of the video I noticed that the points have related x and y values that go in some sort of shape that goes all the way around without crossing the other sides. did anybody else notice that? And does that also mean that any shape like that makes a rectangle?
(1 vote)
• There is a pattern, which has to do with the fact that the rectangle is actually a square.

Going clockwise around the square,
it just so happens to be that the sum of the 𝑥-coordinate of one corner and the 𝑦-coordinate of the next corner is constant,
and the difference between the 𝑦-coordinate of one corner and the 𝑥-coordinate of the next corner is also constant.

This is true for all squares.
• Actually, the answer is C, since when you calculate the side lengths, you find out that they are equal, meaning that the shape is a square.
(1 vote)
• You're partially correct.
Yes, the shape has 4 same side length. However, you have 2 things that you made a mistake in.

1. A square is also a rectangle. Thus claiming "No" is incorrect.

2. The prove is not sufficient enough to show that ABCD is a rectangle. Notice that a rhombus also has 4 same side length, and a rhombus doesn't have to have 4 right angles.

Tip when verifying your answer: You can attempt to show that there are no other possible solutions that fits the claim you selected.
• how do i use this in real life? Just wondering.
• How exactly would taking the opposite reciprocal confirm that it is a 90 degree angle?
(1 vote)
• Perpendicular lines have slopes that are the opposite reciprocal of each other. Perpendicular lines form 90 degree angles when they intersect.