Question

1. Show that the triangle with vertices A (8,5). B (1, -2) and C(-3, 2) is a right angled triangle. Find its area.​

Answer 1

Answer:

• 14 units²

Step-by-step explanation:

Plot the points.

According to the attached we can see the triangle is right.

Use distance formula to find the length of AB and BC:

• $AB=\sqrt{(1-8)^2+(-2-5)^2}=\sqrt{7^2+7^2}=7\sqrt{2}$
• $BC=\sqrt{(-3-1)^2+(2+2)^2}=\sqrt{4^2+4^2}=2\sqrt{2}$

Find the area:

• $A = 1/2(AB*BC)$
• $A = 1/2(7\sqrt{2}*2\sqrt{2}) = 14$