Question

Quadrilateral JKLM was dilated according to the rule
DO,(x,y) to create the image quadrilateral J'K'L'M', which is shown on the graph.



What are the coordinates of vertex J of the pre-image?

(0, -4)
(0, -1)
(0, 0)
(0, 4)

Answer 1

The coordinates of point J' is (0,-2) which represent the image of J
let J (x,y) ⇒⇒⇒⇒ J' (x',y') = (0 , -2 )

The graph was dilated according to the rule:
(x,y) ⇒⇒⇒ ( 0.5x , 0.5y)

so, for the x coordinate
∴ x' = 0.5 x  ⇒⇒⇒ x = 2x' = 2*0 = 0

for the y coordinate
y' = 0.5 y ⇒⇒⇒ y = 2y' = 2 * (-2) = -4

∴ The coordinates of J is ( 0 , -4 )
∴ The correct answer is the first option

Answer 2

The coordinates of vertex J of the pre-image is (0, -4)

Transformation

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

Dilation is the increase or decrease in the size of a figure by a factor k. The dilated figure has the same shape as the original figure.

Given the dilation (x, y) ⇒ [(1/2)x, (1/2)y] on quadrilateral JKLM to produce quadrilateral J'K'L'M'.

The vertex J' has coordinates (0, -2). Hence the coordinates of J = (0, -4)

The coordinates of vertex J of the pre-image is (0, -4)

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