Question

Help me please, this is really hard.

Answer 1

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

Explanation:

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

The scale factor is
`(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+(1)/(4)(-3-5),-5+(1)/(4)(7+5)).`

`D(-3,7)=(5+(1)/(4)(-8),-5+(1)/(4)(12)).`

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

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

To find B',

`D(9,3)=(5+(1)/(4)(9-5),-5+(1)/(4)(3+5)).`

`D(9,3)=(5+(1)/(4)(4),-5+(1)/(4)(8)).`

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

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

To find C',

`D(-7,-5)=(5+(1)/(4)(-7-5),-5+(1)/(4)(-5+5)).`

`D(-7,-5)=(5+(1)/(4)(-12),-5+(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).