Question

What’s point B’ What’s point C’ After being dilated by a scale factor 1.5?

Answer 1

Given:

The given figure is dilated by a scale factor 1.5.

To find:

The coordinates of B' and C'.

Solution:

If a figure is dilated by a scale factor k at point (a,b), so the rule of transformation is

$(x,y)\to (k(x-a)+a,k(x-b)+b)$

From the given figure it is clear that A(3,-3), B(-2,2) and C(-3,-5).

The figure is dilated by a scale factor 1.5 at point A(3,-3), so the rule of transformation is

$(x,y)\to (1.5(x-3)+3,1.5(x-(-3))+(-3))$

$(x,y)\to (1.5(x-3)+3,1.5(x+3)+(-3))$

$(x,y)\to (1.5(x)-4.5+3,1.5(x)+4.5-3)$

$(x,y)\to (1.5x-1.5,1.5x+1.5)$

Using this rule, we get

$B(-2,2)\to B'(1.5(-2)-1.5,1.5(2)+1.5)$

$B(-2,2)\to B'(-3-1.5,3+1.5)$

$B(-2,2)\to B'(-4.5,4.5)$

And

$C(-3,-5)\to C'(1.5(-3)-1.5,1.5(-5)+1.5)$

$C(-2,2)\to C'(-4.5-1.5,-7.5+1.5)$

$C(-2,2)\to C'(-6,-6)$

Therefore, the coordinates of B' and C' are B(-4.5,4.5) and C'(-6,-6).