Question

1. triangle nop below will be dilated with the origin as the center of dilation and a scale factor of 1/2. what will be the coordinates of the vertices of the dilated image, △nop? a. n(4, 4), o(8, 4), p(16, 20) b. n(1, 2), o(2, 2), p(4, 10) c. n(1, 1), o(2, 1), p(4, 5) d. n(1, 1), o(1, 1), p(3, 5)

Explanation:

Step1: Identify original coordinates

From the graph, the coordinates of $\triangle NOP$ are $N(2,2)$, $O(4,2)$, $P(8,10)$.

Step2: Apply dilation formula

When dilating a point $(x,y)$ with the origin as the center of dilation and a scale - factor $k$, the new coordinates $(x',y')$ are given by $(x',y')=(k\times x,k\times y)$. Here $k = \frac{1}{2}$.
For point $N(2,2)$: $N'(\frac{1}{2}\times2,\frac{1}{2}\times2)=(1,1)$
For point $O(4,2)$: $O'(\frac{1}{2}\times4,\frac{1}{2}\times2)=(2,1)$
For point $P(8,10)$: $P'(\frac{1}{2}\times8,\frac{1}{2}\times10)=(4,5)$

Answer:

C. $N'(1,1),O'(2,1),P'(4,5)$