Question

Triangle EFG has vertices at E(-4,4), F(-2, 6), and G(-2, 2). If the triangle is dilated by a scale factor of [Select] and is then rotated 180°, what will be the coordinates of F' after the series of transformations?

a) (1,-3)
b) (-1, -3)
c) (1,3)
d) (1,3)

Answer 1

a) (1, -3)

Step-by-step explanation:

dilated by scale factor of 1/2 [2/2 = 1, 6/2 = 3]

rotated 180: (x, y) → (-x, -y)

(-1, 3) → (1, -3)

The answer is A.

Answer 2

Assuming a dilation factor of 2.0 for EFG, point F would first be dilated to (-4, 12) and then, after a 180° rotation, its coordinates would be F' (4, -12). The coordinates (4, -12) do not match any of the given options, suggesting an error in the question or options.

Step-by-step explanation:

To determine the coordinates of the point F' after the series of transformations given for triangle EFG with vertices E(-4,4), F(-2, 6), and G(-2, 2), we need to apply a dilation by a scale factor and then a 180° rotation. Unfortunately, the scale factor is not provided in the question, so we'll assume a scale factor of 2.0 as mentioned in the reference. First step is the dilation. Using a scale factor of 2.0, we double the coordinates of F(-2, 6), resulting in F1(-4, 12). This is the dilation step. Second step is the rotation. To rotate a point 180° around the origin, we invert the signs of its coordinates. Applying this to F1(-4, 12), we get F' (4, -12). However, none of the given options matches F' (4, -12). There seems to be an error either in the question or the options provided. Given the provided information and assuming the dilation factor as 2.0, the correct coordinates of point F' are (4, -12), which is not an option provided in the question. The student may need to double-check the original question or the possible answers.