Question

The coordinates of both the pre-image and image of quadrilateral JKLM are listed in the table

below.
Which rule best represents this dilation?
A- (x, y) -> (4/11 x, 4/11 y)
B- (x,y) -> (3/22 x, 3/22 y)
C- (x, y) -> (11/4 x, 11/4 y)
D- (x, y) -> (22/3 x, 22/3 y )

Answer 1

Option C.

Explanation:

From the table attached,

Pre-image coordinates J(-8, 2) → Image coordinates J'(-22, 5.5)

J(-8, 2) → J'(-22, 5.5)

Since, rule for the dilation of a point is,

(x, y) → (kx, ky) [Here k = scale factor of dilation]

Therefore, kx = -22

k(-8) = -22

k =
`(-22)/(-8)`

k = 2.75

So the scale factor should be 2.75

From the given options,

Option A.

(x, y) →
`(4)/(11)(x, y)`

→ 0.36(x, y)

But value of k should be 0.36

Therefore, Incorrect option.

Option B.

(x, y) →
`(3)/(22)(x, y)`

→ 0.14(x, y)

k = 0.14

But the value of k should be 2.75

Incorrect option.

Option C.

(x, y) →
`(11)/(4)(x, y)`

→ 2.75(x, y)

k = 2.75

Therefore, this option is correct.

Option D.

(x, y) →
`(22)/(3)(x, y)`

→ 7.33(x, y)

k = 7.33

But the scale factor should be 7.33

Incorrect option.