Question

Draw the image of \triangle ABC△ABCtriangle, A, B, C under a dilation whose center is AAA and scale factor is \dfrac{1}{4} 4 1 ​ start fraction, 1, divided by, 4, end fraction.

Answer 1

Answer: (1, 1), (3, 4) and (1, 2)

Explanation:

Answer 2

The dilated triangle A ′B ′C ′ under a dilation with center P(2,2)mand a scale factor of
`(1)/(4)`. A'
`(-(1)/(2),(-1)/(2))` , B'
`((7)/(2), (-1)/(2) )`, C' (1.2, 2.55)

To find the new coordinates of the dilated triangle A'B'C' under a dilation with center P and a scale factor of 4, we'll use the formula I provided earlier.

Let's assume that the coordinates of the vertices of triangle ABC are as follows:

A(0,0), B(8,0), C'(4.8, 8.4)

Now, let's assume that the center of dilation is P(2, 2), and the scale factor is k =
`(1)/(4)`

The new coordinates A', B', and C' can be calculated using the dilation formula:

`x_(A') = x_p + (1)/(4) (x_A+x_P)`

`y_(A') = y_p + (1)/(4) (y_A+y_P)`

Applying this formula to each vertex:

A'= (2+
`(1)/(4)` (0-2), 2 +
`(1)/(4)` (0-2)) =
`(-(1)/(2),(-1)/(2))`

B' = (2 +
`(1)/(4)` (8 - 2), 2+
`(1)/(4)` (0 - 2)) =
`((7)/(2), (-1)/(2) )`

C' = (2 +
`(1)/(4)` (4. 8 - 2), 2+
`(1)/(4)` (8.4 - 2)) ≈ (1.2, 2.55)

Now, you can plot these new coordinates on a graph to visualize the dilated triangle A ′B ′C ′.