Question

the graph shows triangles fgh and fgh. which of the following transformations maps fgh onto fgh? translation right 9 units and up 7 units; translation right 16 units and up 4 units; reflection across the x - axis; reflection across the y - axis; rotation 90° clockwise around the origin; rotation 90° counterclockwise around the origin; rotation 180° around the origin

Explanation:

Step1: Find coordinates of F, G, H

Let's take point F: original F is at (-2, 2), F' is at (7, 9).
G: original G is at (-8, -2), G' is at (1, 5).
H: original H is at (-6, -7), H' is at (3, 0).

Step2: Calculate horizontal and vertical shifts

For F: Horizontal shift: \(7 - (-2) = 9\), Vertical shift: \(9 - 2 = 7\).
Check G: \(1 - (-8) = 9\), \(5 - (-2) = 7\).
Check H: \(3 - (-6) = 9\), \(0 - (-7) = 7\).
So shift right 9, up 7.

Answer:

translation right 9 units and up 7 units