Question

A triangle abc has vertices at a(3,2), b(4,0) and c(8,2). show that the triangle is right angled.

Answer 1

To determine whether the triangle ABC is right-angled, calculate the slopes of the lines AB and AC and examine their product. If the product is -1, the triangle is right-angled. In this case, the triangle ABC is not right-angled.

Step-by-step explanation:

To determine whether the triangle ABC is right-angled, we can examine the slopes of the lines connecting the vertices.

1. First, find the slopes of the lines AB and AC using the formula: slope = (change in y)/(change in x).
2. Next, calculate the products of the slopes of AB and AC. If the products equal -1, then the triangle is right-angled.
3. Finally, determine the slopes and products for the given coordinates. If the product of the slopes is -1, the triangle is right-angled.

In this case, the slope of AB is -2 and the slope of AC is 0. The product of these slopes is 0, which is not equal to -1. Therefore, the triangle ABC is not right-angled.