Answer:
Part A: The two types of types of transformation are
1) Rotation of 11.3° about (1, 2)
2) By algebraic transformation
Part B:
Rotation by 11.3° and T(2 - y)×1/2 + x, 0)
Part C: The transformation that can be used to transform f(x) to g(x) is T(2 - y)×1/2 + x, 0)
Step-by-step explanation:
The coordinates through which the linear function f(x) passes = (1. 3) and (3, 13)
The coordinates through which the linear function g(x) passes = (1, 3) and (1, 13)
The equation for f(x) in slope and intercept form. y = m·x + c is given as follows;
The slope, m = (13 - 3)/(3 - 1) = 5
The equation in point and slope form is y - 3 = 5×(x -1)
y = 5·x - 5 + 3 = 5·x - 3
y = 5·x - 3
The equation for g(x) in slope and intercept form. y = m·x + c is given as follows;
The slope, m = (13 - 3)/(1 - 1) = ∞
∴ The equation in point and slope form is x = 1
Therefore, the two equations meet at the point (1, 2)
The transformation that can be used to transform f(x) to g(x) is T(2 - y)×1/2 + x, 0)
2) Another transformation that can be used is to rotate f(x) by the vertex angle as follows
Vertex angle is 90° - tan⁻¹(m) = 90° - tan⁻¹(5) ≈ 11.3°
Rotation of f(x) by 11.3° about (1, 2) gives g(x)
Hope this helped!
