Question

1. which of the following represents a translation 2 units left and 7 units up? 2. if q(0,0) is translated by (x,y)→(x - 4,y - 2), what are the new coordinates of q? 3. describe what happens to a triangle if it is reflected over the y - axis. will its shape or size change? 4. what is the image of p(3,5) after reflection over the x - axis?

Explanation:

Step1: Determine translation rule for 1

Left - subtract from x, up - add to y. So rule is $(x,y)\to(x - 2,y+7)$.

Step2: Calculate new coordinates for 2

Substitute $x = 0$ and $y = 0$ into $(x,y)\to(x - 4,y - 2)$. We get $x'=0 - 4=-4$ and $y'=0 - 2=-2$. So $Q'(-4,-2)$.

Step3: Analyze reflection over y - axis for 3

Reflection over y - axis changes sign of x - coordinate. The rule is $(x,y)\to(-x,y)$. Shape and size do not change as it is a rigid transformation.

Step4: Find image after x - axis reflection for 4

Reflection over x - axis changes sign of y - coordinate. For $P(3,5)$, the image is $P'(3,-5)$.

Answer:

1. $(x,y)\to(x - 2,y+7)$
2. $Q'(-4,-2)$
3. The x - coordinates of all points change sign. Shape and size do not change.
4. $P'(3,-5)$