Question

The point A = (7,4) is dilated from the origin by a scale factor r = 3. What are the coordinates of A' ?

Answer 1

Given:

The coordinates of point A are (7,4).

It is dilated from the origin by a scale factor r = 3.

To find:

The coordinates of A'.

Solution:

If a figure is dilated from the origin by a scale factor k, then

$(x,y)\to (kx,ky)$

Here, the figure is dilated from the origin by a scale factor 3, so the rule of dilation is given by:

$(x,y)\to (3x,3y)$

Using this rule, we get

$A(7,4)\to A'(3(7),3(4))$

$A(7,4)\to A'(21,12)$

Therefore, the coordinates of point A' are (21,12).