Question

6.figure abcd with vertices a(1,2), b(5,2), c(4,4), and d(2,4) is dilated by a scale factor of 3 to form a’b’c’d’. what is the length of a’b’?

Explanation:

Step1: Find the length of AB

Use the distance formula for two - points $(x_1,y_1)$ and $(x_2,y_2)$ which is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For points $A(1,2)$ and $B(5,2)$, $x_1 = 1,y_1 = 2,x_2 = 5,y_2 = 2$. Then $AB=\sqrt{(5 - 1)^2+(2 - 2)^2}=\sqrt{4^2+0^2}=4$.

Step2: Use the dilation property

When a figure is dilated by a scale factor $k$, the length of each side is multiplied by $k$. Here $k = 3$. So $A'B'=k\times AB$.
Since $AB = 4$ and $k = 3$, then $A'B'=3\times4 = 12$.

Answer:

12