Question

Help me please, this is really hard.

Answer 1

The points of new triangle is (3,-2), (6,-3) and (2,-5).

Step-by-step explanation:

The given points in the triangle A(-3,7), B(9,3) and C(-7,-5).

The scale factor is $\frac{1}{4}$ and centered at point (5,-5).

The formula to dilate a point that is not centered on a origin is given by,

D(x,y)=(h+t(x-h),k+t(y-t)).

where (h,k) is the center point.

To find A',

$D(-3,7)=(5+\frac{1}{4}(-3-5),-5+\frac{1}{4}(7+5)).$

$D(-3,7)=(5+\frac{1}{4}(-8),-5+\frac{1}{4}(12)).$

D(-3,7)=(5-2, -5+3).

D(-3,7)=(3,-2).

To find B',

$D(9,3)=(5+\frac{1}{4}(9-5),-5+\frac{1}{4}(3+5)).$

$D(9,3)=(5+\frac{1}{4}(4),-5+\frac{1}{4}(8)).$

D(9,3) = (5+1,-5+2).

D(9.3)=(6,-3).

To find C',

$D(-7,-5)=(5+\frac{1}{4}(-7-5),-5+\frac{1}{4}(-5+5)).$

$D(-7,-5)=(5+\frac{1}{4}(-12),-5+\frac{1}{4}(0)).$

D(-7,-5)=(5-3,-5+0).

D(-7,-5)=(2,-5).

∴ The points of new triangle is (3,-2), (6,-3) and (2,-5).