Question

Triangle XYZ is shown on the coordinate grid.

Which statements are true about triangle XYZ?


XY measures √26units.

YZ measures √56 units.

ZX measures √34 units.

XYZ is an isosceles triangle.

XYZ is a right triangle.

XYZ is a scalene triangle.

Answer 1

Distance between two points
`(x_(1),y_(1)), (x_(2),y_(2))` in two dimensional coordinate plane is given by:
`\sqrt{(x_(2)-x_(1))^2+(y_(2)-y_(1))^2`

`XY=√((4+1)^2+(4-5)^2)\\\\ XY=√(25 +1)\\\\ XY=√(26)\\\\ YZ=√((4+2)^2+(4-0)^2)\\\\ YZ=√(36 +16)\\\\ YZ=√(52)\\\\ YZ=2√(13)\\\\ XZ=√((-2+1)^2+(5-0)^2)\\\\ XZ=√(1+25)\\\\ XZ=√(26)\\\\ Also, (XY)^2+(XZ)^2=(√(26))^2+(√(26))^2=52=(YZ)^2`

As, Converse of Pythagorean theorem states that if sum of squares of any two adjacent sides in a triangle is equal to Square of length of third side, then the triangle is right angled triangle.

The true statement about the triangle XYZ is

1. XY measures √26units.

2. XYZ is an isosceles triangle.

3. XYZ is a right triangle.