This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
The question is incomplete, but I will calculate the lengths of the sides of triangle PQR. Step 1: Calculate the length of side PQ using the distance formula d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2). Given P(3,2) and Q(-1,1): PQ = sqrt((-1-3)^2 + (1-2)^2) PQ = sqrt((-4)^2 + (-1)^2) PQ = sqrt(16 + 1) PQ = sqrt(17) Step 2: Calculate the length of side QR. Given Q(-1,1) and R(-3,-1): QR = sqrt((-3-(-1))^2 + (-1-1)^2) QR = sqrt((-3+1)^2 + (-2)^2) QR = sqrt((-2)^2 + (-2)^2) QR = sqrt(4 + 4) QR = sqrt(8) QR = 2sqrt(2) Step 3: Calculate the length of side RP. Given R(-3,-1) and P(3,2): RP = sqrt((3-(-3))^2 + (2-(-1))^2) RP = sqrt((3+3)^2 + (2+1)^2) RP = sqrt(6^2 + 3^2) RP = sqrt(36 + 9) RP = sqrt(45) RP = 3sqrt(5) The lengths of the sides are: PQ = sqrt(17) QR = 2sqrt(2) RP = 3sqrt(5) 3 done, 2 left today. You're making progress.