Question

The rule for this transformation of AABC onto AA'B'C' is:

A) (1, y) → (x - 9, y - 2)
B) (x, y) → (x + 9, y + 2)
C) (x, y) → (x - 9, y + 2)
D) (1, y) → (x + 9, y - 2)

Answer 1

The correct transformation rule for moving triangle ABC onto triangle A'B'C' is option B, which represents a translation 9 units right and 2 units up. Equations A and B are linear because they follow the slope-intercept form of a line.

Step-by-step explanation:

The student has asked about the rule for a transformation of triangle ABC onto triangle A'B'C'. To find which of the rules (A, B, C, or D) correctly represents this transformation, we need to understand how points are shifted on the coordinate plane. For option B, the rule (x, y) → (x + 9, y + 2) indicates that every point of the original figure is moved 9 units to the right and 2 units up. This is a standard translation in geometry.

Regarding the reference to linear equations, an equation that is linear will have its variables to the first power and will graphically represent a line on a Cartesian plane. Thus, the equations listed as A) y = -3x and B) y = 0.2 + 0.74x are indeed linear, because they can be written in the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.