Question

Line segment RS has endpoints R(-2, 4) and S(-4,-1).
Line segment R"S" has endpoints R"(3, -3) and S" (5,2).
Name the transformations that map line segment RS to line segment R"S".

Answer 1

Answer:

The transformation that map line RS to line R"S" is " rotation of 180° about the origin, followed by a translation (x, y) → (x + 1, y + 1)" ⇒ B

Step-by-step explanation:

Let us revise some transformation

• If the point (x, y) rotated about the origin by angle 180° counterclockwise, then its image is (-x, -y) ⇒ R(180, O) (x, y) → (-x, -y)

• If the point (x, y) translated horizontally to the right by h units then its image is (x + h, y) ⇒ T (x, y) → (x + h, y)

• If the point (x, y) translated vertically up by k units then its image is (x, y + k) ⇒ T (x, y) → (x, y + k)

∵ The coordinates of the point R = (-2, 4)

∵ The coordinates of point R" = (3, -3)

→ Both coordinates in R" have opposite signs then R

∴ R rotated 180° about the origin ⇒ using the 1st rule above

∴ R' = (2, -4)

→ Find the difference between the x-coordinate of R" and x-coordinate

  of R'

∵ xR" - xR' = 3 - 2 = 1

→ By using the 2nd rule above

∴ R' translated 1 unit to the right

→ Find the difference between the y-coordinate of R" and y-coordinate

  of R'

∵ yR" - yR' = -3 - (-4) = -3 + 4 = 1

→ By using the 3rd rule above

∴ R' translated 1 unit up

∴ The rule of translation is T(x, y) ⇒ (x + 1, y + 1)

Let us use these 2 rules on S to find S"

∵ The coordinates of the point S = (-4, -1)

∵ S is rotated 180° around the origin

→ By using the 1st rule above, opposite the signs of its coordinates

∴ S' = (4, 1)

∵ S' translated 1 unit right

→ By using the 2nd rule above, add its x-coordinate by 1

∵  S' translated 1 unit up

→ By using the 3rd rule above, add its y-coordinate by 1

∴ S" = (4 + 1, 1 + 1)

∴ S" = (5,2)

→ That means the rules of transformation of point R is right

The transformation that map line RS to line R"S" is " rotation of 180° about the origin, followed by a translation (x, y) → (x + 1, y + 1)"