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
You're on a roll — Let's enlarge this quadrilateral! Step 1: Identify the coordinates of the original quadrilateral PQRS. From the graph, the coordinates are: P = (-3, 1) Q = (-1, 3) R = (2, -2) S = (-2, -2) The center of enlargement is C = (2, 1) and the scale factor is k = -(1)/(2). Step 2: Apply the enlargement formula to each vertex. The formula for enlargement with center (a,b) and scale factor k is P'(x', y') = (a + k(x-a), b + k(y-b)). Here, (a,b) = (2,1) and k = -(1)/(2). For P (-3, 1): x_P' = 2 + (-(1)/(2))(-3 - 2) = 2 + (-(1)/(2))(-5) = 2 + (5)/(2) = (4)/(2) + (5)/(2) = (9)/(2) = 4.5 y_P' = 1 + (-(1)/(2))(1 - 1) = 1 + (-(1)/(2))(0) = 1 + 0 = 1 So, P' = (4.5, 1) For Q (-1, 3): x_Q' = 2 + (-(1)/(2))(-1 - 2) = 2 + (-(1)/(2))(-3) = 2 + (3)/(2) = (4)/(2) + (3)/(2) = (7)/(2) = 3.5 y_Q' = 1 + (-(1)/(2))(3 - 1) = 1 + (-(1)/(2))(2) = 1 - 1 = 0 So, Q' = (3.5, 0) For R (2, -2): x_R' = 2 + (-(1)/(2))(2 - 2) = 2 + (-(1)/(2))(0) = 2 + 0 = 2 y_R' = 1 + (-(1)/(2))(-2 - 1) = 1 + (-(1)/(2))(-3) = 1 + (3)/(2) = (2)/(2) + (3)/(2) = (5)/(2) = 2.5 So, R' = (2, 2.5) For S (-2, -2): x_S' = 2 + (-(1)/(2))(-2 - 2) = 2 + (-(1)/(2))(-4) = 2 + 2 = 4 y_S' = 1 + (-(1)/(2))(-2 - 1) = 1 + (-(1)/(2))(-3) = 1 + (3)/(2) = (2)/(2) + (3)/(2) = (5)/(2) = 2.5 So, S' = (4, 2.5) Step 3: List the coordinates of the enlarged quadrilateral P'Q'R'S'. The new coordinates are: P' = (4.5, 1) Q' = (3.5, 0) R' = (2, 2.5) S' = (4, 2.5) Step 4: Draw the quadrilateral P'Q'R'S'. To draw the quadrilateral, plot the points P'(4.5, 1), Q'(3.5, 0), R'(2, 2.5), and S'(4, 2.5) on the same graph paper. Then, connect the points in order: P' to Q', Q' to R', R' to S', and S' to P'. The coordinates of the enlarged quadrilateral are P'(4.5, 1), Q'(3.5, 0), R'(2, 2.5), S'(4, 2.5). What's next? Send 'em!