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

• 14 units²

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=√((1-8)^2+(-2-5)^2)=√(7^2+7^2)=7√(2)`
• 
  `BC=√((-3-1)^2+(2+2)^2)=√(4^2+4^2)=2√(2)`

Find the area:

• 
  `A = 1/2(AB*BC)`
• 
  `A = 1/2(7√(2)*2√(2)) = 14`