Question

1) Triangle T1 is transformed into triangle T2 by

a. dilation with scale factor of 1/2
b. reflection over the y-axis
c. translation

2) and triangle T2 is transformed into trinagle T3 by
a. dilation with scale factor 1/2
b. reflection over the x-adis
c. rotation

Answer 1

1) The correct option is;

b. Reflection over the y-axis

2) The correct option is;

a. Dilation by a scale factor of 1/2

Explanation:

1) The rule for reflection over the y-axis is given as follows;

Given the point of the preimage before the reflection = (x, y), the point of the image after the reflection will be (-x, y)

The coordinate of a point on T1 is (-2, 4). The coordinate of similar point in T2 is (2, 4) which satisfies the rule for reflection over the y-axis

2) The length of a side in triangle T2 is given by the formula for finding the length, l, of segments between coordinate points as follows;

`l = \sqrt{\left (y_(2)-y_(1) \right )^(2)+\left (x_(2)-x_(1) \right )^(2)}`

Point 1, (x₁, y₁) = (2, 4)

Point 2, (x₂, y₂) = (6, 2)

The length = √((2 - 4)² + (6 - 2)²) = 2·√5

The length of the corresponding side in T3 is given as follows;

Point 1, (x₁, y₁) = (1, 2)

Point 2, (x₂, y₂) = (3, 1)

The length = √((1 - 2)² + (3 - 1)²) = √5

The length of of a side T3 = 1/2 of the length of a side of T2

Therefore. triangle T2 is transformed into triangle T3 by dilation with a scale factor of 1/2.