Question

1. write the coordinates for △pqr after a translation of 10 units left and 2 units up. in what quadrant is △pqr located now?

a) quadrant i
c) quadrant ii
b) quadrant iii
d) quadrant iv

1. two figures, a and b, are shown. select all of the sequences of transformations that will map a onto b.

a) reflection over the line y = x
b) rotation 180 degrees clockwise about the origin
c) reflection over the y - axis followed by a translation 8 units down
d) translation 8 units down followed by a 180 - degree rotation about the origin
e) translation 4 units to the right and 8 units down followed by a reflection over the line x = 2
f) translation 11 units down and 5 units to the right followed by a reflection over the line y = - 5

1. write an algebraic rule for a translation that moves a triangle 5 units to the right and 6 units up.

a) (x,y)-->(x + 5,y + 6)
c) (x,y)-->(x - 5,y + 6)
b) (x,y)-->(x + 5,y - 6)
d) (x,y)-->(x - 5,y - 6)
set a
geometry
hope high school
sy 2025 - 2026

Explanation:

10.

Step1: Recall translation rule

A translation of 10 units left and 2 units up changes the coordinates of a point $(x,y)$ to $(x - 10,y + 2)$. Without knowing the original coordinates of $\triangle PQR$, we can still analyze the quadrant based on the general effect of the translation. If the original triangle was in a lower - right quadrant, moving 10 units left (subtracting 10 from the x - coordinate) and 2 units up (adding 2 to the y - coordinate) will likely move it to Quadrant II.

Step1: Analyze each transformation option

• A) reflection over the line $y=x$: This will swap the x and y coordinates of each point of figure A. By visual inspection, this will not map A onto B.
• B) rotation 180 degrees clockwise about the origin: The rule for a 180 - degree rotation about the origin is $(x,y)\to(-x,-y)$. This will not map A onto B.
• C) reflection over the y - axis followed by a translation 8 units down: Reflection over the y - axis changes $(x,y)$ to $(-x,y)$ and then translating 8 units down gives $(-x,y - 8)$. This can map A onto B.
• D) translation 8 units down followed by a 180 - degree rotation about the origin: Translating 8 units down gives $(x,y-8)$ and then rotating 180 degrees about the origin gives $(-x,-(y - 8))=(-x,-y + 8)$. This will not map A onto B.
• E) translation 4 units to the right and 8 units down followed by a reflection over the line $x = 2$: Translating 4 units to the right and 8 units down gives $(x + 4,y-8)$. Reflecting over the line $x = 2$: Let the point after translation be $(x_1,y_1)=(x + 4,y-8)$. The distance from $x_1$ to $x = 2$ is $d=x_1-2=(x + 4)-2=x + 2$. The new x - coordinate after reflection is $2-(x + 2)=-x$. This can map A onto B.
• F) translation 11 units down and 5 units to the right followed by a reflection over the line $y=-5$: Translating gives $(x + 5,y-11)$. Reflecting over the line $y=-5$: Let the point after translation be $(x_1,y_1)=(x + 5,y-11)$. The distance from $y_1$ to $y=-5$ is $d=y_1+5=(y - 11)+5=y-6$. The new y - coordinate after reflection is $-5-(y - 6)=1 - y$. This can map A onto B.

Step1: Apply translation rule

A translation of 5 units to the right means adding 5 to the x - coordinate of each point of the triangle, and a translation of 6 units up means adding 6 to the y - coordinate of each point. The algebraic rule for a translation that moves a point $(x,y)$ 5 units to the right and 6 units up is $(x,y)\to(x + 5,y+6)$.

Answer:

C. Quadrant II

11.