Question

C (-1,-7), A (1,4), T (5, 1). What kind of triangle is CAT? Calculate the area and the perimeter of CAT.

Answer 1

A) Right Angle Triangle

B) 25 units²

C) (15 + 5√5) units

Figure Their Length:

`\sf Distance \ between \ two \ points = √((x_2 - x_1)^2 + (y_2 - y_1)^2)`

Distance between C and A

`\rightarrow \sf CA = √((1 - (-1))^2 + (4 - (-7))^2) \ = \ 5√(5)`

Distance between C and T

`\rightarrow \sf CT = √((-1-5)^2+(-7-1)^2) \ = \ 10`

Distance between A and T

`\rightarrow \sf AT = √((1-5)^2 +(4-1)^2) \ = \ 5`

Part A:

When drawn on graph, we can identify it is a right angle triangle.

Or use Pythagoras Theorem:

10² + 5² = (5√5)²

125 = 125... Hence it is a right angle triangle confirmed.

Part B:

Area of triangle = ½ × base × height = ½ × 10 × 5 = 25 units²

Part C:

Total Sum or measure of all sides: 5 + 10 + 5√5 = 15 + 5√5 units