Question

Rhombus JKLM is dilated with center (-4, 7) and scale factor to produce rhombus J'K'L'M'. Fill in the table below to determine the missing coordinates.

Answer 1

Transforming the rhombus JKLM by dilation with a scale factor of 1/4 and center at D(0, 3), gives;

• J'(0, 2.5)

• L(-16, 19)

What formula can be used to find the coordinates of the image following a dilation?

From the question, we have;

Center of dilation = D(0, 3)

Scale factor of dilation = 1/4

The given points are;

• J(0, 1), L'(-4, 7)

The required points are J' and L

Given that the x-coordinate of J is the same as the center of dilation, we have;

The x-coordinate of J' = 0

The formula for finding the coordinates following a dilation is presented as follows;

Dilation;

(x, y) → (k(x - a) + a, k(y - b) + b)

Where;

Center of dilation = (a, b)

Scale factor = k

Therefore;

J(0, 1)

J'(0.25•(0 - 0) + 0, 0.25•(1 - 3) + 3)

The coordinates of J' is therefore;

• J'(0, 2.5)

L'(-4, 7) = L(0.25(x - 0) + 0, 0.25(y - 3) + 3)

0.25(x - 0) + 0 = -4

Therefore;

x = -16

0.25•(y - 3) + 3 = 7

y - 3 = (7 - 3)/0.25 = 16

y = 19

• The coordinates of L is therefore (-16, 19)

Learn more about dilation transformation here:

https://brainly.com/question/14263066

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