Answer:
ΔPTS≅ΔRTA by AAS axiom of congruency
Step-by-step explanation:
Consider ΔPQA and ΔRQS
∠PQA=∠RQS (Vertically Opposite Angles)
∠QAP=∠QSR (Complementary of two equal angles, ∠RAT and∠PST)
Due to angle sum property of a triangle, we come to the conclusion that
∠APQ=∠SRQ
Consider ΔPTS and ΔRTA
TA=TS (Given)
∠RAT=∠PST(Given)
∠APQ=∠SRQ (Proved above)
Therefore, ΔPTS≅ΔRTA by AAS axiom of congruency.
Answer:
D, see description below.
There is a possible typo in the problem since these points have slope 25/23.
Step-by-step explanation:
To find the slope of a line, calculate the distance between points with a ratio of vertical to horizontal distance. This is done using the formula:

Here the points are (-4,-14) and (19,11). Substitute and simplify.

I think there is a typo in your points (-4,-14) and (19,11) because the answer doesn't align to the answer choices. But based on them, I would answer D or 24/23 since it's the closest value.
The height will be six times what is on the drawing.
6 4/5 x 6 = 36 24/5 = 40 4/5 inches tall.
14/38 simplified would be 7/19