Question

Coordinates A (1, 2), B (3, 2) and C (3, 5) are connected to form ΔABC. If F is plotted at (6, 11) would ΔEFD be similar to ΔABC? Explain.

A) No, not all of the corresponding legs have been multiplied by the same scale factor.
B) Yes, ED is twice the length of AC.
C) Yes, corresponding parts have been multiplied by the same scale factor.
D) No, there is no way to draw similar triangles since AC and ED are not whole numbers.

Answer 1

I believe it to be C if I am wrong pls correct me

Answer 2

Coordinates A (1, 2), B (3, 2) and C (3, 5) which forms a Right triangle.

AB=2 units, BC=3 units, →→By looking at the diagram depicted in coordinate plane.

AC=
`√(2^2+3^2)=√(13)` →→→ By using Pythagorean theorem

Now in ΔDEF, if Point F is located at (6,11),∠F=90°

DF=6 units,EF=4 units →→By looking at the diagram depicted in coordinate plane.

DF=
`√(6^2+4^2)=√(52)` →→→ By using Pythagorean theorem

In ΔEFD and ΔABC

∠F=∠B=90°

`(AB)/(EF)=(BC)/(DF)=(AC)/(DE)=(1)/(2)`

ΔEFD ~ ΔABC by SAS or SSS

Option (C) Yes, corresponding parts have been multiplied by the same scale factor.