The below question can be found in Hard practice question set, question 13 of geometry strategy guide. i have 3 major doubts regarding this single question.
Doubt 1:
I was wondering if there is an alternative way to work around this problem. since it's a trapezoid, can we make use of area of trapezoid formula i.e A=(Base1+Base2)/2 * Hieght. If so, could you please arrive at the solution with the formula? (I tried working out, no luck)
The reason i am looking for an alternate way to solve the problem is because the current method which is used in the book is bit too length. first we find the slope (Y Value)(Use slope forumla) , then find the area of the whole rectangle, then find the individual triangle lengths (i.e find length and width using distance formula), then subtract the respective triangles from the rectangle. Puff! just too much work!
Doubt 2:
We know the x coordinate of point P has to be=0. Now, would be fair to guess that the y coordinate is a/2, purely because distance from R to x coordinate is a, hence p(which is half way), could be around a/2. therefore coordinate of p are (0,a/2).
Doubt 3:
I am keen in knowing how the author found the pattern of rectangle from this trapezoid. Is it something we need to always try to look for when trapezoid is embedded in a coordinate plane? Clearly my initial few minutes were spent on solving the problem using the formula above! Never, recognized the pattern!
Thank you.
