Question

Use the measure of the sides of triangle ABC to classify the triangle by its sides A(-1,3) B(-3,5) C(3,2)

Answer 1

Answer:

The triangle is a scalene triangle that has all three sides having different lengths

Step-by-step explanation:

The given vertices (and their coordinates) of the triangle are;

A(-1, 3)

B(-3, 5)

C(3, 2)

The equation for finding the lengths of a segment, l, given the coordinates, x, y is presented as follows;

$l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}$

For segment AB, when, (x₁, y₁) = A(-1, 3) and (x₂, y₂) = B(-3, 5),  we have;

$l = \sqrt{\left (5-3 \right )^{2}+\left (-3-(-1) \right )^{2}} = 2\cdot\sqrt{2}$

Length of segment AB = 2·√2

For segment AC, when, (x₁, y₁) = A(-1, 3) and (x₂, y₂) = C(3, 2),  we have;

$l = \sqrt{\left (2-3 \right )^{2}+\left (3-(-1) \right )^{2}} = \sqrt{17}$

Length of segment AC = √17

For segment BC, when, (x₁, y₁) = B(-3, 5) and (x₂, y₂) = C(3, 2),  we have;

$l = \sqrt{\left (2-5 \right )^{2}+\left (3-(-3) \right )^{2}} = 3 \cdot \sqrt{5}$

Length of segment AC = 3·√5

The triangle is a scalene triangle that has all three sides having different lengths.