Triangle ABC has vertices point A (2,1) point B (-2,2) and point C (-3,-1) after dilation triangle A'B'C' has vertices point A' (4,2). Point C' (-6,-2) determine the scale factor for the dilation of triangle ABC with a center point of dilation at the origin(0,0)

Answer 1

To find the scale factor, we can use the formula:

scale factor = distance between A' and the origin / distance between A and the origin

Let's calculate the distance between A' and the origin first. The coordinates of A' are (4,2), and the origin is (0,0). We can use the distance formula:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

distance = sqrt((4 - 0)^2 + (2 - 0)^2)
distance = sqrt(16 + 4)
distance = sqrt(20)

Now, let's calculate the distance between A and the origin. The coordinates of A are (2,1), so we can use the distance formula again:

distance = sqrt((2 - 0)^2 + (1 - 0)^2)
distance = sqrt(4 + 1)
distance = sqrt(5)

Finally, we can calculate the scale factor:

scale factor = distance between A' and the origin / distance between A and the origin
scale factor = sqrt(20) / sqrt(5)
scale factor = sqrt(20/5)
scale factor = sqrt(4)
scale factor = 2

Therefore, the scale factor for the dilation of triangle ABC with a center point of dilation at the origin is 2.