Question

Match each set of vertices to the triangle they form. Which triangle is formed by the vertices a (2, 4), b (4, 5), c (3, 6)?

1) right scalene
2) acute equilateral
3) acute isosceles
4) obtuse scalene
5) right isosceles

Answer 1

The vertices a(2, 4), b(4, 5), and c(3, 6) form a right scalene triangle.

Step-by-step explanation:

The vertices a(2, 4), b(4, 5), and c(3, 6) form a right scalene triangle.

First, we can find the lengths of the sides using the distance formula: c = sqrt((x2 - x1)^2 + (y2 - y1)^2).

Using this formula, we can find that side ab is approximately 2.236 units, side bc is approximately 1.414 units, and side ac is approximately 2.236 units.

Since all three sides have different lengths and one angle is 90 degrees, the triangle is classified as a right scalene triangle.