Question

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

Answer 1

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 =
`(2)/(3)`

(x, y) →
`((2)/(3)x, (2)/(3)y)`

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

A(8, 6) →
`A'((2* 8)/(3),(2* 6)/(3))`

→ A'(5.3, 4)

B(12, 12) →
`B'((12* 2)/(3), (12* 2)/(3))`

→ B'(8, 8)

Now we can get the image of segment AB after dilation by a scale factor of
`(2)/(3)`.