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
Step 1: Apply the dilation formula for the x-coordinate. The formula for the x-coordinate of a dilated point A'(p,q) from A(x,y) with center P(a,b) and scale factor k is p = a + k(x - a). Given A(5,9), P(2,4), and k=3: p = 2 + 3(5 - 2) p = 2 + 3(3) p = 2 + 9 p = 11 Step 2: Apply the dilation formula for the y-coordinate. The formula for the y-coordinate of a dilated point A'(p,q) from A(x,y) with center P(a,b) and scale factor k is q = b + k(y - b). Given A(5,9), P(2,4), and k=3: q = 4 + 3(9 - 4) q = 4 + 3(5) q = 4 + 15 q = 19 Step 3: Calculate the value of 2p + q. Now substitute the values of p=11 and q=19 into the expression 2p + q: 2p + q = 2(11) + 19 2p + q = 22 + 19 2p + q = 41 The value of 2p + q is 41. Drop the next question.