a) Δ ABC is rotated around the origin by angle 180° and then translated 1
unite to the right and 3 units up
b) R (O , 180°) and T (x + 1 , y + 3)
Step-by-step explanation:
* Lets revise some transformation
- If point (x , y) rotated about the origin by angle 180° then its image
is (-x , -y)
- If the point (x , y) translated horizontally to the right by h units
then its image is (x + h , y)
- If the point (x , y) translated horizontally to the left by h units
then its image is (x - h , y)
- If the point (x , y) translated vertically up by k units
then its image is = (x , y + k)
- If the point (x , y) translated vertically down by k units
then its image is (x , y - k)
* Lets solve the problem
∵ Δ ABC change its place from 2nd quadrant to the 4th quadrant
and reverse its direction Point A up and its image A" down
∵ No change in its size
∴ Triangle ABC rotates 180° clockwise around the origin
# Remember : There is no difference between rotating 180° clockwise
or anti-clockwise around the origin
∵ The vertices of Δ ABC are:
# A = (-3 , 5)
# B = (-3 , 2)
# C = (-1 , 2)
∵ If point (x , y) rotated about the origin by angle 180° then its image
is (-x , -y)
∴ A'' = (3 , -5)
∴ B'' = (3 , -2)
∴ C'' = (1 , -2)
∴ Triangle ABC rotates 180° around the origin to form ΔA"B"C"
∵ The vertices of Δ A'B'C are:
# A' = (4 , -2)
# B' = (4 , 1)
# C' = (2 , 1)
- By comparing the x-coordinates and y-coordinates of points of
Δ A''B''C'' and Δ A'B'C' we will find that every x-coordinate add by 1
and every y-coordinate add by 3
∵ 4 - 3 = 1 and 2 - 1 = 1 ⇒ x- coordinates
∵ -2 - (-5) = -2 + 5 = 3 and 1 - (-2) = 1 + 2 = 3 ⇒ y-coordinates
∴ ΔA''B''C'' translates to the right 1 unite and up 3 units to form
Δ A'B'C'
a) Δ ABC is rotated around the origin by angle 180° and then
translated 1 unite to the right and 3 units up
b) R (O , 180°) and T (x + 1 , y + 3)
