Question

Determine the coordinates of the vertices of the figure J K L M after a dilation with a scale factor of 5 from the image J K L M, centered at the origin.

a) J(-10, -10), K(5, -10), L(5, 10), M(-10, 10)
b) J(-2, -2), K(1, -2), L(1, 2), M(-2, 2)
c) J(-50, -50), K(25, -50), L(25, 50), M(-50, 50)
d) J(-5, -5), K(2.5, -5), L(2.5, 5), M(-5, 5)

Answer 1

After dilating the original figure by a scale factor of 5 from the origin, the coordinates of the vertices are J(-50, -50), K(25, -50), L(25, 50), M(-50, 50); hence the correct answer is option (c).

Step-by-step explanation:

To determine the coordinates of the vertices after a dilation with a scale factor of 5 centered at the origin, each coordinate of the vertices is multiplied by the scale factor. The process involves scaling both the x and y coordinates of each point by the factor of 5.

1. Dilate point J: Multiply both coordinates of J(-2, -2) by 5 to get J(-10 * 5, -10 * 5) = J(-50, -50).
2. Dilate point K: Multiply both coordinates of K(1, -2) by 5 to get K(5 * 5, -10 * 5) = K(25, -50).
3. Dilate point L: Multiply both coordinates of L(1, 2) by 5 to get L(5 * 5, 10 * 5) = L(25, 50).
4. Dilate point M: Multiply both coordinates of M(-2, 2) by 5 to get M(-10 * 5, 10 * 5) = M(-50, 50).

The correct coordinates after dilation are hence option (c): J(-50, -50), K(25, -50), L(25, 50), M(-50, 50).