Question

1. if a triangle is reflected over the y-axis and then dilated by a scale factor of 2, what will be the new coordinates of the point (2,3)?

a. (-4,6)
b. (-2,-6)
c. (4,3)
d. (4,6)

1. which transformation would you apply to map a rectangle at (1,1), (1,3), (3,3), and (3,1) to (4,5), (4,7), (6,7), and (6,5)?

a. translation 3 units right and 4 units up
b. rotation 90 degrees clockwise
c. dilation by a scale factor of 2
d. reflection over the x-axis

Explanation:

First Question

Step1: Reflect over y-axis

When reflecting a point $(x,y)$ over the y-axis, the new x-coordinate is $-x$. For $(2,3)$, this gives $(-2, 3)$.

Step2: Dilate by scale factor 2

To dilate a point $(x,y)$ by scale factor $k$, multiply both coordinates by $k$. For $(-2,3)$ and $k=2$:
$(-2 \times 2, 3 \times 2) = (-4, 6)$

Step1: Compare corresponding coordinates

Take the first original point $(1,1)$ and target point $(4,5)$:

• Horizontal change: $4 - 1 = 3$ (3 units right)
• Vertical change: $5 - 1 = 4$ (4 units up)

Verify with another pair: $(1,3)$ to $(4,7)$:

• $4-1=3$, $7-3=4$, same shift applies to all points.

Answer:

a. $(-4,6)$

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Second Question