Question

on your own graph paper, draw the original and dilated figures. (dok 3)

for the questions 1–6, find the coordinates of the vertices of the dilated figure. (dok 2)

1 a: (-1, 1) a: ______
b: (-1, 4) b: ______
c: (1, 4) c: ______
d: (3, 1) d: ______
scale factor: 4

2 a: (-6, 5) a: ______
b: (3, 5) b: ______
c: (3, -4) c: ______
d: (-6, -4) d: ______
scale factor: \\(\frac{1}{3}\\)

3 a: (-10, 0) a: ______
b: (0, 10) b: ______
c: (8, 5) c: ______
scale factor: \\(\frac{4}{5}\\)

4 a: (-1, 7) a: ______
b: (1, 7) b: ______
c: (5, 5) c: ______
d: \\((5, \frac{1}{2})\\) d: ______
e: (1, -3) e: ______
f: (-1, -3) f: ______
g: \\((-5, \frac{1}{2})\\) g: ______
h: (-5, 5) h: ______
scale factor: 2

5 a: (-8, 7) a: ______
b: (-4, 7) b: ______
c: (-2, 3) c: ______
d: (-6, 3) d: ______
scale factor: \\(\frac{3}{2}\\)

6 a: (-4, 12) a: ______
b: (6, -2) b: ______
c: (-14, -2) c: ______
scale factor: \\(\frac{1}{2}\\)

for questions 7–10, find the scale factor. (dok 2)

7 a: (-3, 2) a: (-10.5, 7)
b: (1, 2) b: (3.5, 7)
c: (1, -3) c: (3.5, -10.5)
d: (-3, -3) d: (-10.5, -10.5)
scale factor: ______

8 a: (-6, 9) a: (-2, 3)
b: (3, 12) b: (1, 4)
c: (6, 3) c: (2, 1)
d: (-9, 0) d: (-3, 0)
scale factor: ______

9 a: (0, -3) a: (0, -2)
b: (6, 0) b: (4, 0)
c: (0, 3) c: (0, 2)
scale factor: ______

10 a: (-2, 6) a: (-10, 30)
b: (2, 6) b: (10, 30)
c: (3, 3) c: (15, 15)
d: (2, 0) d: (10, 0)
e: (-2, 0) e: (-10, 0)
f: (-3, 3) f: (-15, 15)
scale factor: ______

for questions 11 and 12, determine whether or not abcd is a dilation of abcd. (dok 3)

11 a: (-2, 5) a: (-1, 2)
b: (8, 8) b: (4, 4)
c: (12, 0) c: (6, 0)
d: (2, -6) d: (1, -3) ______

12 a: (0, 8) a: (0, 4)
b: (5, 8) b: \\((\frac{5}{2}, 4)\\)
c: (5, -3) c: \\((\frac{5}{2}, -\frac{3}{2})\\)
d: (0, -3) d: \\((0, -\frac{3}{2})\\) ______

Explanation:

Let's solve question 1 as an example (finding coordinates of dilated figure with scale factor 4):

Step1: Recall dilation rule

To dilate a point \((x, y)\) with scale factor \(k\), the new coordinates are \((k \cdot x, k \cdot y)\). Here, \(k = 4\).

Step2: Dilate point A: \((-1, 1)\)

Multiply each coordinate by 4: \(x\)-coordinate: \(4 \times (-1) = -4\), \(y\)-coordinate: \(4 \times 1 = 4\). So \(A' = (-4, 4)\).

Step3: Dilate point B: \((-1, 4)\)

\(x\)-coordinate: \(4 \times (-1) = -4\), \(y\)-coordinate: \(4 \times 4 = 16\). So \(B' = (-4, 16)\).

Step4: Dilate point C: \((1, 4)\)

\(x\)-coordinate: \(4 \times 1 = 4\), \(y\)-coordinate: \(4 \times 4 = 16\). So \(C' = (4, 16)\).

Step5: Dilate point D: \((3, 1)\)

\(x\)-coordinate: \(4 \times 3 = 12\), \(y\)-coordinate: \(4 \times 1 = 4\). So \(D' = (12, 4)\).

Step1: Recall scale factor formula

For a dilation, scale factor \(k=\frac{\text{coordinate of image}}{\text{coordinate of original}}\) (for corresponding coordinates). Let's use point \(A\): \(A(-3, 2)\), \(A'(-10.5, 7)\).

Step2: Calculate \(k\) using \(x\)-coordinates

\(k=\frac{-10.5}{-3}= 3.5=\frac{7}{2}\). Check with \(y\)-coordinates: \(\frac{7}{2}=3.5\). Verify with other points (e.g., \(B(1, 2)\), \(B'(3.5, 7)\): \(\frac{3.5}{1}=3.5\), \(\frac{7}{2}=3.5\)).

Step1: Use scale factor formula

Take point \(A(-6, 9)\), \(A'(-2, 3)\). Calculate \(k\) for \(x\)-coordinate: \(\frac{-2}{-6}=\frac{1}{3}\). Check \(y\)-coordinate: \(\frac{3}{9}=\frac{1}{3}\). Verify with \(B(3, 12)\), \(B'(1, 4)\): \(\frac{1}{3}\), \(\frac{4}{12}=\frac{1}{3}\).

Answer:

\(A': (-4, 4)\), \(B': (-4, 16)\), \(C': (4, 16)\), \(D': (12, 4)\)

---

Let's solve question 7 (finding scale factor):