Question

quadrilateral qrst is dilated and translated to form similar figure qrst. what is the scale factor for the dilation?

Explanation:

Step1: Find corresponding sides

Take QR and Q'R'. QR length: from x=-1 to x=4, so 5 units. Q'R' length: from x=-1 to x=1, so 2 units? Correction: Recheck grid—QR is base of large trapezoid: from (-1,0) to (4,0)? No, Q is (-1,0), R is (4,0): length 5. Q' is (-1,2), R' is (1,2): length 2? Wait no, Q'R' is top of small trapezoid: distance between (-1,2) and (1,2) is 2. QR is distance between (-1,0) and (4,0) is 5? No, wait scale factor is small/large or large/small? Wait similar figures: scale factor = image/original. Q'R'S'T' is image, QRST original. Q'R' length: 2, QR length: 5? No, wait another side: QS vs Q'S'. QS is vertical? No, Q is (-1,0), S is (4,-5)? No, better: Q to R in original: let's count grid squares for horizontal side QR: from x=-1 to x=4 is 5 squares. Q' to R' is from x=-1 to x=1 is 2 squares? No, wait maybe I misread: original QRST has base QR of length 4 (from x=0 to x=4?), no—wait the small figure Q'R'S'T' has horizontal side Q'R' of length 2 (2 grid units), original QR has length 4 (4 grid units)? Oh yes! If Q'R' is 2 and QR is 4, scale factor is 2/4=1/2.

Step2: Calculate scale factor

Scale factor = length of image side / length of original side = 2/4 = 1/2.

Answer:

$\frac{1}{2}$