Question

1. figure abcd is shown on the coordinate plane below. the figure will be dilated by a scale factor of 2, with the center of the dilation at the origin. the resulting image will be figure abcd. what will be the coordinates of vertex a? a (-5,6) b (-3,6) c (-3,8) d (-6,8) 3. a transformation maps △abc to △abc. if △abc is similar but not congruent to △abc, which transformation occurred? a a rotation about the origin b a reflection over the y - axis c a dilation with a scale factor not equal to 1 d a translation of 1 unit in both the x and y directions

Explanation:

Question 12

Step1: Find coordinates of A

From the graph, vertex \( A \) has coordinates \( (-3, 4) \).

Step2: Apply dilation with scale factor 2

Dilation with center at origin and scale factor \( k \) transforms a point \( (x, y) \) to \( (kx, ky) \). Here, \( k = 2 \), so for \( A(-3, 4) \), \( A' = (2\times(-3), 2\times4) = (-6, 8) \)? Wait, no, wait. Wait, maybe I misread the coordinates. Wait, looking at the grid, let's recheck. Wait, the x-coordinate of A: from the origin (0,0), moving left 3 units? Wait, no, the grid lines: the x-axis, each grid is 1 unit. Let's see, point A: x is -3? Wait, no, maybe the x-coordinate is -3? Wait, no, let's look at the graph again. Wait, the figure ABCD: B is at (-3, 1), A is above B. So B is (-3, 1), A is (-3, 4)? Wait, no, the y-coordinate: B is at y=1, A is at y=4, x=-3? Wait, then dilation by 2: x becomes -32 = -6, y becomes 42 = 8? But option D is (-6,8). Wait, but let's check again. Wait, maybe I made a mistake. Wait, the original coordinates: let's see the grid. The x-axis: from -10 to 10, y-axis from -10 to 10. Point A: looking at the graph, A is at (-3, 4)? Wait, no, maybe x is -3? Wait, the grid lines: each square is 1 unit. So A is at (-3, 4). Then dilation by 2: (-32, 42) = (-6, 8), which is option D. Wait, but let's check the options. Option D is (-6,8). So that's the answer.

• Rotation (A) and reflection (B) and translation (D) preserve congruence (shape and size), so the image is congruent to the original.
• Dilation with scale factor ≠ 1 (C) changes the size, so the triangles are similar (same shape, different size) but not congruent.

Answer:

D. \((-6, 8)\)

Question 3