Question

Please help much appreciated!!!!!!!!!!!!!

Answer 1

The triangle is an isosceles triangle

Explanation:

Let's get some definitions out of the way:

A scalene triangle is a triangle in which all three sides are in different lengths, and all three angles are of different measures.

An isosceles triangle is a triangle in which two sides are equal lengths, and angles opposite to equal sides are equal

An equilateral triangle is a triangle in which all three sides are equal and all three angles are equal

Let's determine the lengths of each of the three sides in ΔXYZ

The distance formula for the distance between any two points (x1, y1) and (x2, y2) is given by

d² = (x2 - x1)² + (y2 - y1)²
So the distance = the square root of the above expression - d

To find length of XY, take points X(4, 2) and Y(2, -2)
Length XY

`√(4-2)^2 + (2 - (-2)^2)\\\\= \sqrt {{4} + {16}}\\\\= √(20)`

Length YZ with Y(2, -2) and Z(-2, 0):


`= \sqrt {(-2 - 2)^2 + (0 - (-2))^2}\\\\ = \sqrt {(-4)^2 + (2)^2}\\\\ = \sqrt {{16} + {4}}\\\\= √(20)`

length XZ with X(4, 2) and Z(-2, 0):

`= \sqrt {(-2 - 4)^2 + (0 - 2)^2}\\\\= \sqrt {(-6)^2 + (-2)^2}\\\\= \sqrt {{36} + {4}}\\\\= \sqrt {40}`

So in triangle XYZ we have two sides equal.
These are XY and YZ
The third side is different

So the triangle is an isosceles triangle