Question

The coordinates P(0, 1), Q(3, 2), R(5, -4) form a right triangle. True or False?
Please show me how do do these type of problems.

Answer 1

Hang on for a minute...

Answer 2

I don't know if you'll be able to view that or not but, basically you can use that calculator to plot the points.

Answer 3

Then you find the distance between the two leg segments

Answer 4

Okay, but what if I can't tell if it's a right triangle by looking at it

Answer 5

The only way to know for sure is by making calculations.

Answer 6

Actually, that is not a good link

Answer 7

Okay :0

Answer 8

Sorry. I don't know why but it won't produce the right links at the moment. Desmos is broken.

Answer 9

Oh no!):

Answer 10

Hang on...

Answer 11

https://www.desmos.com/calculator/ylu1f7r9or

Answer 12

Okay, if you go to that link, you'll notice that the points form what appears to be a right triangle, however, we won't know for sure until we perform a reciprocal slopes test.

Answer 13

Notice that the point (3,2) is common to both legs of the possible right triangle. The legs of the right triangle need to have reciprocal slopes in order for the triangle to be right.

Answer 14

So find the slopes of between the following sets of points:

(0,1) and (3,2)

(3,2) and (5,-4)

Answer 15

If the product of the slopes equal -1, then you know that the triangle is right.

Answer 16

Is that where I use y-y/x-x

Answer 17

Yes use

\[m = \frac{y_2 - y_1}{x_2 - x_1}\]

Answer 18

Can I use any number to start with?

Answer 19

You can start with any point you want to but you still have to find the slopes using the proper sets of points.

Answer 20

First find the slope between points (0,1) and (3,2)

Answer 21

Let me know what you get

Answer 22

I got 1/3 and -3/1 so does that mean it's a right triangle since it's the reciprocal?

Answer 23

Hang on, let me make sure those are correct.

Answer 24

Since 1/3*(-3) = -1, then the slopes are reciprocals of each other, which mean they are perpendicular to each other. In other words, they form a 90 degree angle. If one of the angles of a triangle is 90 degrees, then the triangle is a right triangle.

Answer 25

Why didn't I find the slope of (0,1) and (5,4)? Was it just because that was the middle coordinate?

Answer 26

Because if you can prove one of the angles of a triangle is 90 degrees, then the triangle is right. You don't have to do anything else afterwards.

Answer 27

There is another quick way just find the the distance between the points using distance formula ... After u find the distance of all 3 sides of the triangle ... U can simply use the Pythagoras theorem and check whether it is right angle... Hope u know about the theorem .... AB^2= BC^2 + AC^2 ....... You'll be guessing how to substitute the values u can c that AB will obviously have a greater value .. Therefore out of the 3 distances the greater number will be AB ... That's it

Answer 28

In this case, the points are already given so finding the appropriate slopes is quicker than finding the distance between the points. Try finding the distance between the points. You'll see that it is much more difficult of a task than you think.

Answer 29

Haha yes actually it is ... Very quick :) but if at all there are other kinds of triangle given to find out example equi or isosceles distance formula has to be used ... Or is there a quicker way ?

Answer 30

This is alternative quicker way is of the slope