The shape of the image of ΔABC following a dilation by a scale factor of [tex]\dfrac{2}{3}[/tex] is the same as the shape of ΔABC but the sizes of the sides of ΔA'B'C' are [tex]\dfrac{2}{3}[/tex] smaller
The correct options with regards the given statements are;
- The measure of ∠B and ∠B' are equal is True
- The coordinates of A and A' are the same is True
Reasons:
The dilation lengths of the sides of ΔABC are AB, AC, BC
The given scale factor of dilation = [tex]\dfrac{2}{3}[/tex]
Therefore;
The lengths of the sides of ΔA'B'C' are [tex]\dfrac{2}{3} \cdot \overline {A'B'}[/tex], [tex]\dfrac{2}{3} \cdot \overline {A'C'}[/tex], [tex]\dfrac{2}{3} \cdot \overline {B'C'}[/tex]
Which gives;
[tex]\dfrac{\overline{A'B'}}{\overline{AB}}} = \dfrac{\overline{A'C'}}{\overline{AC}}} = \dfrac{\overline{B'C'}}{\overline{BC}}} = \dfrac{2}{3}[/tex]
Given that the ratio of the corresponding sides of ΔABC and ΔA'B'C' are equal, ΔABC is similar to ΔA'B'C' by triangle similarity theorem
Therefore;
∠A = ∠A', ∠B = ∠B', and ∠C = ∠C' by definition of triangle similarity
Which gives;
The statement; The measure of ∠B and ∠B' are equal is True
Second part;
The center of dilation of ΔABC is point A, therefore, the distance between point A and point A' following a dilation is zero
Therefore, given that there is no difference, we have;
The coordinates of point A = The coordinates of point A'
Therefore;
The statement, the coordinates of A and A' are the same is True
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https://brainly.com/question/2584916
