Question

1. a 5\ x 8\ picture was enlarged to a 12.5\ x 20\ picture. what was the scale factor used? transformations maze! directions: use the points a(-7, 2), b(2, 4), c(-8, -6), d(6, -3), and e(-2, -1) to complete the maze. use your solutions to navigate through the maze. *ccw = counterclockwise start! reflect point a over the x - axis (7, 2) translate point e under the rule (x, y) → (x - 1, y + 7) (10, 5) dilate point b using a scale factor of k = 5/2 (4, 8) rotate point e 270° ccw about the origin (-7, -2) (7, -2) (-3, 6) (3, -6) (-9, -1) (5, 10) (2, 1) dilate point e using a scale factor of k = 3 (-6, -3) rotate point d 180° about the origin (-6, 3) translate point c under the rule (x, y) → (x - 1, y + 5) (-7, 1) reflect point e over the y - axis (6, 3) (-3, -6) (3, 6) (3, 6) (-7, -1) (2, -1) (-2, -1) end! (-2, 1) dilate point d using a scale factor of k = 2 (2, -1) rotate point b 270° ccw about the origin (4, -2) dilate point d using a scale factor of k = 1/3 (6, 8) (6, -8) (-6, 8) (-4, -2) (-2, -4) (-4, 2) (2, -1) translate point b under the rule (x, y) → (x + 4, y + 2) (8, 6) rotate point c 90° ccw about the origin (6, 8) dilate point c using a scale factor of k = 3/2 (-1, -1) translate point a under the rule (x, y) → (x + 8, y - 3) (-2, -7) (2, 7) (4, -3) (-4, 3) (3, 4) (-1, 1) (1, -1) rotate point a 180° about the origin (7, -2) translate point d under the rule (x, y) → (x - 2, y) (4, 3) dilate point c using a scale factor of k = 1/2 (-8, 6) reflect point c over the y - axis (2, -4) (-2, -4) (0, 0) (-4, -3) (-3, -4) (-4, 2) (8, -6) reflect point b over the x - axis (-4, -2) translate point e under the rule (x, y) → (x - 2, y - 1) (-2, -4) reflect point b over the y - axis (4, -2) rotate point b 90° ccw about the origin © gina wilson (all things algebra®, llc) 2017

Explanation:

Problem 8: Scale Factor Calculation

Step 1: Identify corresponding sides

The original picture is \( 5'' \times 8'' \) and the enlarged one is \( 12.5'' \times 20'' \). We can take the length or the width to find the scale factor. Let's take the length: original length \( l_1 = 5'' \), enlarged length \( l_2 = 12.5'' \).

Step 2: Calculate scale factor

The scale factor \( k \) is the ratio of the enlarged length to the original length. So \( k=\frac{l_2}{l_1}=\frac{12.5}{5} \).
Simplifying, \( \frac{12.5}{5} = 2.5 \) (we can also check with the width: \( \frac{20}{8}=2.5 \), so it's consistent).

Answer:

The scale factor used is \( 2.5 \) (or \( \frac{5}{2} \)).