Question

1. a point is dilated by a given scale factor (k). use the scale factor (k) to write the ordered pairs after the dilation.

a. a(1,5) and k = 2 so a (__, __)
b. b(4,2) and k = ½ so b (__, __)
c. a(0, 8) and k = 1/2 so a (__, __)
d. b(9,12) and k = 1/3 so b (__, __)
e. a(-8, 3) and k = 3 so a (__, __)
f. b(7, -3) and k = 4 so b (__, __)

Explanation:

Part a

Step1: Recall dilation formula

To dilate a point \((x,y)\) with scale factor \(k\), the new point \((x',y')\) is given by \((x',y')=(k\times x,k\times y)\). For point \(A(1,5)\) and \(k = 2\), we multiply each coordinate by \(k\).

Step2: Calculate new coordinates

For the \(x\)-coordinate: \(x'=2\times1 = 2\)
For the \(y\)-coordinate: \(y'=2\times5=10\)

Step1: Recall dilation formula

The formula for dilation is \((x',y')=(k\times x,k\times y)\). For point \(B(4,2)\) and \(k=\frac{1}{2}\), we multiply each coordinate by \(k\).

Step2: Calculate new coordinates

For the \(x\)-coordinate: \(x'=\frac{1}{2}\times4 = 2\)
For the \(y\)-coordinate: \(y'=\frac{1}{2}\times2 = 1\)

Step1: Recall dilation formula

Using the dilation formula \((x',y')=(k\times x,k\times y)\) for point \(A(0,8)\) and \(k=\frac{1}{2}\).

Step2: Calculate new coordinates

For the \(x\)-coordinate: \(x'=\frac{1}{2}\times0 = 0\)
For the \(y\)-coordinate: \(y'=\frac{1}{2}\times8 = 4\)

Answer:

\(A'(2,10)\)

Part b