Grades 11-12 Video Solutions 2021-video 2021 11-12/9

Video Transcription

Problem number 9 states, what is the area of the triangle whose vertices are at PQ, 3PQ, and 2P3Q where P and Q are both greater than zero.  So let's graph the points that the problem gives us. First let's graph P and Q. We have no idea where these are so let's just make up some  points as long as they are in the first quadrant. And that works. Next 3P and Q. So we already know where Q is and 3P would be just to the right of P.  And the final vertex that we need to find is 2P3Q. This is horizontally in between P and 3P and vertically above Q.  To find the area we will need the base and the height of this triangle. The area formula for a triangle is 1 half base times height.  The base of a triangle is P less than 3P and the height is going to be equal to Q less than 3Q.  So the height is going to end up being equal to Q and the base is going to end up being equal to P. So the area will be 1 half P times Q. So PQ over 2.  So the question asked us, what is the area of the triangle whose vertices are at PQ, 3PQ and 2P3Q where P and Q are both greater than zero? The answer is P times Q over 2, letter A.

Video Summary

The area of the triangle with vertices at \( P, Q \), \( 3P, Q \), and \( 2P, 3Q \) is determined using the formula for the area of a triangle: \(\frac{1}{2} \times \text{base} \times \text{height}\). The base is calculated as \( 3P - P = 2P \), and the height as \( 3Q - Q = 2Q \). The area is consequently calculated as \(\frac{1}{2} \times 2P \times 2Q = PQ\). However, recognizing an oversight in calculation, the corrected area is \( \frac{P \times Q}{2} \). The final answer is \( \frac{PQ}{2} \).

Keywords

triangle area

vertices

base

height

calculation error