Question

ANSWER PLEASE! ITS HARD!!Graph the image of triangleXYZ after a dilation with a scale factor of
1
4
and the origin as its center. Then enter an algebraic rule to describe the dilation. Express any fractions in the rule for the dilation in simplest form.

Answer 1

Relax this isn't really that hard. We're given a triangle with coordinates

X(4,4), Y(12,12), Z(4,12)

and we're told to dilate it around the origin by scale factor 1/4.   The origin part makes it easy; this just means we multiply all the coordinates by 1/4.

So our new triangle is

X'(1,1), Y'(3,3), Z'(1,3)

which we plot in red.

Is that third page asking for the lengths?  We have

X'Y' is the hypotenuse of a right triangle with legs 2 and 2, so

|X'Y'| = 2√2

|Y'Z'| is 3-1 = 2

|Z'X'| = 2

The rule is

(x,y) → (x/4, y/4)

Answer 2

Scale factors are used to enlarge or reduce the size of a shape

The coordinates of the dilated triangle are (1,1), (3,3) and (1,3)

The coordinates of the triangle are given as:

$X = (4,4)$

$Y = (12,12)$

$Z = (4,12)$

The scale factor of dilation is given as:

$k=\frac 14$

The coordinates of the new triangle after dilation are calculated as follows:

$X' = (4,4) \times \frac 14$

$X' = (1,1)$

$Y' = (12,12) \times \frac 14$

$Y' = (3,3)$

$Z' = (4,12) \times \frac 14$

$Z' = (1,3)$

So, the dilation rule is:

$(x,y) \to \frac 14(x,y)$

Hence, the coordinates of the dilated triangle are (1,1), (3,3) and (1,3)

See attachment for the image of the triangle

Read more about dilations at:

https://brainly.com/question/10253650