Question

The triangle formed by the vertices A(-4, 0), B(4, 0) and C(0,3) is

• A. isosceles triangle
• B. equilateral triangle
• C. scalene triangle
• D. right-angled triangle

Answer 1

The Correct Option is A

To determine the type of triangle, we first calculate the lengths of its sides using the distance formula: \[ \text{Distance between two points} (x_1, y_1) \text{ and } (x_2, y_2) = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] - Distance \( AB \): \[ AB = \sqrt{(4 - (-4))^2 + (0 - 0)^2} = \sqrt{8^2} = 8 \] - Distance \( BC \): \[ BC = \sqrt{(4 - 0)^2 + (0 - 3)^2} = \sqrt{4^2 + 3^2} = \sqrt{16 + 9} = \sqrt{25} = 5 \] - Distance \( CA \): \[ CA = \sqrt{(0 - (-4))^2 + (3 - 0)^2} = \sqrt{4^2 + 3^2} = \sqrt{16 + 9} = \sqrt{25} = 5 \] Since \( BC = CA \), the triangle is isosceles. Thus, the triangle formed by the vertices is an isosceles triangle.

The correct option is (A): isosceles triangle