Question

Help please!! Multiple choice geometry coordinates question Question 12

Answer 1

In the attached picture you find the two triangles. To check if the lengths of the sides are the same, we use the formula for the distance between two points:

$d(A,B) = \sqrt{(A_x-B_x)^2+(A_y-B_y)^2}$

If we plug the values for the points of PQR, we have

$\overline{PQ} \approx 5.39$

$\overline{QR} \approx 3.61$

$\overline{PR} \approx 7.07$

Similarly, for STU we have

$\overline{ST} \approx 5.1$

$\overline{TU} \approx 2.24$

$\overline{SU} \approx 6.71$

As you can see, the lengths of the sides do not match, as a triplet, so the two triangles are not congruent.