Question

Point (-3, 1) is translated 3 units left and 3 units up and then dilated by afactor of 12 using the origin as the center of dilation. What is the resultantpoint?

Answer 1

When we translated a point by a units horizontally, we do the following transformation

$(x,y)\to(x+a,y)$

If a is positive the point goes to the right and if a is negative the point goes to the left.

To translate our point 3 units to the left, we subtract 3 from the x coordinate.

$(-3,1)\to(-3-3,1)=(-6,1)$

When we translated a point by b units vertically, we do the following transformation

$(x,y)\to(x,y+b)$

If b is positive the point goes upwards and if b is negative the point goes downwards.

Moving our point 3 units up, we have

$(-6,1)\to(-6,1+3)=(-6,4)$

And when we dilate around the origin with a factor of dilation k, we do the following transformation

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

Dilating our point around the origin by a factor of 1/2, we have

$(-6,4)\to(1/2\cdot(-6),1/2\cdot4)=(-3,2)$

The image of C is C''(-3, 2).