If 3 points form a right angle triangle

You can view as many worked out examples as you want. First you are shown the question. Click Show Answer to view the answer.
Click Show another Example to view another example. The best way to master mathematics is by practice. But practice requires time.
If you don't have the time to practice, you can always view many practice problems completely worked out and become good at it too.

$\text{Determine if the points }A\left(8,8\right)\text{ , }B\left(20,4\right)\text{ and }C \left(7,5\right)\text{ form a right angle triangle.}$

**Answer**

$\text{We will find the distance between each pair of points. If the square of one distance}$

$\text{is the sum of the squares of the other two distances, the 3 points will form a right}$

$\text{angle triangle, otherwise not.}$

$\text{The distance between the points }A\left(8,8\right)\text{ and }B \left(20,4\right)$

$AB=\sqrt{(4-8)^2+(20-8)^2}$

$= \sqrt{(-4)^2+(12)^2}$

$= \sqrt{16+144}$

$= \sqrt{160}$

$\text{So, }(AB)^2= 160$

$\text{The distance between the points }B \left(20,4\right)\text{ and }C \left(7,5\right)$

$BC=\sqrt{(5-4)^2+(7-20)^2}$

$= \sqrt{(1)^2+(-13)^2}$

$= \sqrt{1+169}$

$= \sqrt{170}$

$\text{So, }(BC)^2= 170$

$\text{The distance between the points }C \left(7,5\right)\text{ and }A \left(8,8\right)$

$CA=\sqrt{(8-5)^2+(8-7)^2}$

$= \sqrt{(3)^2+(1)^2}$

$= \sqrt{9+1}$

$= \sqrt{10}$

$\text{So, }(CA)^2=10$

$\text{Since, }(BC)^2 = (AB)^2 + (CA)^2 \text{ , the 3 points form a right angle triangle.}$