Given the vertices of the triangle:
a(0, 3), b(3, 6), c(9, 3)
Let's answer the following questions:
• 1. Reflect over the x-axis
After a reflection over the x-axis, we have the reflection rule:
(x, y) ==> (x, -y)
Thus, the coordinates will be:
a(0, 3) ==> a'(0, -3)
b(3, 6) ==> b'(3, -6)
c(10, 3) ==> c'(9, -3)
After the reflection over the x-axis, the coordinates are:
a'(0, -3), b'(3, -6), c'(9, -3)
• 2. Dilate by 1/3
To dilate by a scale factor of 1/3, we are to multiply all coordinates by 1/3.
We have:
[tex]\begin{gathered} (0*\frac{1}{3},-3*\frac{1}{3})=a^{\prime}^{\prime}(0,-1) \\ \\ (3*\frac{1}{3},-6*\frac{1}{3})=b^{\prime}^{\prime}(1,-2) \\ \\ (9*\frac{1}{3},-3*\frac{1}{3})=c^{\prime\prime}(3,-1) \end{gathered}[/tex]The coordinates after a dilation with a scale factor of 1/3 are:
a''(0, -1), b''(1, -2), c''(3, -1)
• 3. Translate up 4 units.
Apply the rule of translation:
(x, y) ==> (x, y+4)
We have:
(0, -1 + 4) ==> (0, 3)
(1, -2+4) ==> (1, 2)
(3.3, -1+4) ==> (3.3, 3)
The coordinates after a translation up 4 units are:
(0, 3), (1, 2), (3.3, 3)
• 4. ,Is the area of the new image greater or less than the pre-image.
,•
Since the scale factor of dilation is less than 1, the area of the new image will be less than the area of the pre-image.
• 5. Are the figures similar or congruent?
The figures are similar because the only transformations that occured are rigid transformations with a dilation.
The corresponding lengths will have the same ratio while the angles will be congruent.
Similar figures have congruent angles and the ratio of the corresponding side lengths are the same.
Therefore, we can say the figures are similar.
ANSWER:
1). a'(0, -3), b'(3, -6), c'(9, -3)
2). a''(0, -1), b''(1, -2), c''(3, -1)
3). a'''(0. 3), b'''(1, 2), c'''(3.3, 3)
4). The area of the new image is less than the area of the pre-image.
5). The figures are similar
