Question

Describe the dilation of the triangle ABC with a scale factor of 5 and a center point of dilation at the origin of (0,0).

Answer 1

[AI-generated answer — Bot GPT 3.5]

The dilation of triangle ABC with a scale factor of 5 and a center point of dilation at the origin (0,0) means that each point of the original triangle will be multiplied by a factor of 5 to obtain the corresponding point in the dilated triangle.

Let's say the coordinates of triangle ABC are:
A(x₁, y₁)
B(x₂, y₂)
C(x₃, y₃)

After dilation, the coordinates of the dilated triangle A'B'C' will be:
A'(5x₁, 5y₁)
B'(5x₂, 5y₂)
C'(5x₃, 5y₃)

The sides of the original triangle will be multiplied by the same scale factor, resulting in the sides of the dilated triangle being 5 times larger than the sides of the original triangle while the shape and angles remain the same.

Therefore, the dilated triangle ABC with a scale factor of 5 and center point at the origin (0,0) will have sides 5 times longer and the vertices will be located at points 5 times farther from the origin than the corresponding vertices of the original triangle.