Straight Lines
Properties of Triangles
AIEEE 2002
Grade 11
Question:
A triangle with vertices $(4, 0), (-1, -1)$ and $(3, 5)$ is:
(1) Isosceles and right-angled
(2) Equilateral
(3) Right-angled but not isosceles
(4) Isosceles only
Step-by-Step Solution
Key Concept: Compute all three side lengths. Then check if the product of slopes of any two sides $= -1$. If you find $|AB| = |AC|$ and $\angle A = 90^\circ$, it is isosceles and right-angled.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)