What are the coordinates of the vertices of a dilation for triangle ABC at A (-1,-1) B(4,0) and C(2,3). A'B'C' with scale factor 2.5 centered at the origin?

The coordinates of the image of Δ ABC are:

A' (-2.5, -2.5), B' (10, 0), C' (5, 7.5)

Step-by-step explanation:

Let us revise the rule of dilation

If the point (x, y) dilated by scale factor k centered at the origin, then the image of the point is (k x, k y)

We will use this rule to solve the question

∵ The vertices of triangle ABC are A (-1, -1), B (4, 0), C (2, 3)

∵ The scale factor of a dilation is 2.5

∴ k = 2.5

∵ The center is the origin

→ That means multiply each coordinate of the points by 2.5

∴ A' = (-1 × 2.5, -1 × 2.5)

∴ A' = (-2.5, -2.5)

∴ B' = (4 × 2.5, 0 × 2.5)

∴ B' = (10, 0)

∴ C' = (2 × 2.5, 3 × 2.5)

∴ C' = (5, 7.5)

The coordinates of the image of Δ ABC are:

A' (-2.5, -2.5), B' (10, 0), C' (5, 7.5)

x = -4

step-by-step explanation:

- 20 - 4(x + 3) = 4x

=> -20 - 4x - 12 = 4x

=> - 32 -4x = 4x

=> -32 = 4x + 4x

=> - 32 = 8x

=> -32/8 = x

=> -4 = x