Question

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

Answer 1

Answer:

Option C.

Step-by-step 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 = $\frac{-22}{-8}$

k = 2.75

So the scale factor should be 2.75

From the given options,

Option A.

(x, y) → $\frac{4}{11}(x, y)$

       → 0.36(x, y)

But value of k should be 0.36

Therefore, Incorrect option.

Option B.

(x, y) → $\frac{3}{22}(x, y)$

       → 0.14(x, y)

k = 0.14

But the value of k should be 2.75

Incorrect option.

Option C.

(x, y) → $\frac{11}{4}(x, y)$

       → 2.75(x, y)

k = 2.75

Therefore, this option is correct.

Option D.

(x, y) → $\frac{22}{3}(x, y)$

       → 7.33(x, y)

k = 7.33

But the scale factor should be 7.33

Incorrect option.