Question

draw a line to match the coordinate rule to its description.

1. match each coordinate rule to the description of its resulting transformation.

a. (x,y)→(x + 3,y)\ti. translate by the directed line segment from (0,0) to (0,4).
b. (x,y)→(y,x)\tii. translate by the directed line segment from (0,0) to (3,0).
c. (x,y)→(x,y + 4)\tiii. reflect across the line y = x.
d. (x,y)→(-x,-y)\tiv. rotate 180° about the origin.
e. (x,y)→(x - 3,y + 4)\tv. translate up 4 units and left 3 units.
points: 5 points

Explanation:

1. For the transformation $(x,y)\to(x + 3,y)$, adding 3 to the x - coordinate and keeping the y - coordinate the same means translating 3 units to the right, which is equivalent to translating by the directed line segment from $(0,0)$ to $(3,0)$.
2. The transformation $(x,y)\to(y,x)$ swaps the x and y coordinates, which is the rule for reflecting across the line $y = x$.
3. The transformation $(x,y)\to(x,y + 4)$ adds 4 to the y - coordinate and keeps the x - coordinate the same, which means translating 4 units up, equivalent to translating by the directed line segment from $(0,0)$ to $(0,4)$.
4. The transformation $(x,y)\to(-x,-y)$ changes the sign of both the x and y coordinates, which is the rule for rotating 180° about the origin.
5. The transformation $(x,y)\to(x - 3,y + 4)$ subtracts 3 from the x - coordinate (moves 3 units left) and adds 4 to the y - coordinate (moves 4 units up), which means translating up 4 units and left 3 units.

Answer:

A. $(x,y)\to(x + 3,y)$ - ii. Translate by the directed line segment from $(0,0)$ to $(3,0)$.
B. $(x,y)\to(y,x)$ - iii. Reflect across the line $y = x$.
C. $(x,y)\to(x,y + 4)$ - i. Translate by the directed line segment from $(0,0)$ to $(0,4)$.
D. $(x,y)\to(-x,-y)$ - iv. Rotate 180° about the origin.
E. $(x,y)\to(x - 3,y + 4)$ - v. Translate up 4 units and left 3 units.