Question

A dilation maps (2, 3) to (4, 6).

a) What is the scale factor of the dilation?
b) If (-6, 3) is under the same dilation, what would its new coordinate be?

Answer 1

A dilation map has the form:
\[\large (x,y)\to (a\cdot x, a\cdot y)\]

Answer 2

how do I do that

Answer 3

notice that each coordinate is being multiplied by a constant

Answer 4

how would you go from
(2,3) to (4,6) , do you see any relationship between x and y

Answer 5

\[\large (2,3)\to (a\cdot 2, a\cdot 3)\]

Answer 6

multiply

Answer 7

right, multiply by what?

Answer 8

2,3and 4,6

Answer 9

what do you multiply each coordinate of x and y

Answer 10

I don't now see I stuck there

Answer 11

\[\large (2,3)\to ({\color{Red} 2}\cdot 2, {\color{Red} 2}\cdot 3)\]

Answer 12

4,6

Answer 13

\[\large (2,3)\to ({\color{Red} 2}\cdot 2, {\color{Red} 2}\cdot 3)=(4,6)\]

Answer 14

so the scale factor is 2

Answer 15

now the part to the B

Answer 16

\[\large {(2,3)\to ({\color{Red} 2}\cdot 2, {\color{Red} 2}\cdot 3) \\ (-6,3) \to (2\cdot (-6), 2 \cdot 3)}\]

Answer 17

\[\large{ (x,y) \to ({\color{blue} 2}\cdot x, {\color{blue} 2}\cdot y) \\~\\ (-6,3) \to (2\cdot (-6), 2 \cdot 3)} \]