Question

b) Let P and Q be two points on the line x-y + 1 = 0 such that each of them is 5
units far from the origin. Find the coordinates points of the line. Also find the
equations of OP and OQ.​

Answer 1

Step-by-step explanation:

The solution of the linear system is (3,4) and (−4,−3)

So P(3,4) and Q(-4,-3)

The following step consists in calculating the area of a triangle with base PQ and height equal to the distance of the line from the origin, that can be calculated with the formula:

h=|x0−y0+1|(1)2+(−1)2√

where x0 and y0 are the coordinates of the origin. Hence, the distance is equal to 2√2

and the base PQ is equal to (3−(−4))2+(4−(−3))2−−−−−−−−−−−−−−−−−−−−√=72–√

The area of the triangle OPQ is now equal to 12PQ∗h=72