Question

q3 - mathematics gr 8 - section 1 | lesson: describing sequences of transformations for similar figures

1. how does a reflection over the line $y = x$ affect the coordinates of a point $(a,b)$?

○ a. the coordinates become $(-b,-a)$.
○ b. the coordinates stay the same.
○ c. the coordinates switch places to become $(b,a)$.
○ d. the coordinates become $(-a,-b)$.

1. which sequence of transformations maps a rectangle from $(1,2), (1,4), (3,4),$ and $(3,2)$ to $(-2,-4), (-2,-8), (-6,-8),$ and $(-6,-4)$?

○ a. translation by 9 units left and 12 units down
○ b. dilation by scale factor of 2
○ c. translation by 2 units right
○ d. dilation by scale factor of -2

1. what is the result of reflecting a figure over the y-axis?

○ a. the figure is rotated.
○ b. the figure is flipped horizontally.
○ c. the figure is translated.
○ d. the figure is resized.

Explanation:

Step1: Analyze reflection over $y=x$

A reflection over $y=x$ swaps $x,y$ coordinates.
For point $(a,b)$, new coordinates are $(b,a)$.

Step2: Analyze rectangle transformation

Take point $(1,2)\to(-2,-4)$. Calculate scale factor:
$\frac{-2}{1}=-2$, $\frac{-4}{2}=-2$.
Verify with $(1,4)\to(-2,-8)$: $\frac{-2}{1}=-2$, $\frac{-8}{4}=-2$.
This matches dilation by $-2$.

Step3: Analyze reflection over y-axis

Reflection over y-axis flips the figure across the vertical y-axis, which is a horizontal flip.

Answer:

1. c. The coordinates switch places to become $(b,a)$.
2. d. dilation by scale factor of -2
3. b. The figure is flipped horizontally.