Question

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

Answer 1

To describe the dilation of triangle ABC with a scale factor of 5 and the center point of dilation at the origin (0, 0), we can start by considering each vertex of the original triangle ABC separately.

Let's say the coordinates of vertex A in the original triangle are (x₁, y₁). After the dilation, the corresponding coordinates in the dilated triangle will be (5x₁, 5y₁). This is because a scale factor of 5 means that every distance in the dilated figure is 5 times the distance in the original figure.

Similarly, if the coordinates of vertex B in the original triangle ABC are (x₂, y₂), the coordinates in the dilated triangle will be (5x₂, 5y₂). And for vertex C with coordinates (x₃, y₃), the dilated coordinates will be (5x₃, 5y₃).

In summary, each vertex of the original triangle is dilated by a factor of 5 when the center of dilation is at the origin (0, 0). The new coordinates of the vertices are obtained by multiplying the original coordinates by the scale factor 5.

Therefore, the dilated triangle ABC has vertices A'(5x₁, 5y₁), B'(5x₂, 5y₂), and C'(5x₃, 5y₃).