Question

Triangle XYZ is shown on the coordinate grid.


Which statements are true about triangle XYZ? Select three options.

XY measures units.
YZ measures units.
ZX measures units.
XYZ is a right triangle.
XYZ is a scalene triangle.

Answer 1

I don't have the diagram or the coordinates of X, Y, and Z, so I can't tell which three options are true yet. Could you either

- upload the image of the coordinate grid showing triangle XYZ, or
- type the coordinates of the three vertices (X(x1,y1), Y(x2,y2), Z(x3,y3))?

If you want to check them yourself, here are the steps:

1. Find coordinates of X, Y, Z from the grid.
2. Compute each side length with the distance formula:
- XY = sqrt[(x2−x1)^2 + (y2−y1)^2]
- YZ = sqrt[(x3−x2)^2 + (y3−y2)^2]
- ZX = sqrt[(x1−x3)^2 + (y1−y3)^2]
(Lengths are in grid units.)

3. To test for a right triangle:
- Either check slopes of pairs of sides: two sides are perpendicular if their slopes m1 and m2 satisfy m1·m2 = −1 (vertical/horizontal case included),
- Or check Pythagorean theorem: for the three side lengths a, b, c (with c the longest), see if a^2 + b^2 = c^2.

4. To test for scalene: verify all three side lengths are different (no equal lengths).

Send the coordinates or an image and I’ll compute the three true statements.