Question

Draw the image of the following segment after a dilation centered at the origin with a scale factor of 2/3

Answer 1

Answer:

Step-by-step explanation:

Let the ends of the given segment are A and B.

Coordinates of A → (8, 6)

Coordinates of B → (12, 12)

If a point (x, y) is dilated by a scale factor 'k' about the origin, rule to be followed,

(x, y) → (kx, ky)

If k = $\frac{2}{3}$

(x, y) → $(\frac{2}{3}x, \frac{2}{3}y)$

By this rule coordinates of the image points of A and B will be,

A(8, 6) → $A'(\frac{2\times 8}{3},\frac{2\times 6}{3})$

           → A'(5.3, 4)

B(12, 12) → $B'(\frac{12\times 2}{3}, \frac{12\times 2}{3})$

             → B'(8, 8)

Now we can get the image of segment AB after dilation by a scale factor of $\frac{2}{3}$.