Question

The vertices of a triangle are A (2,5) B (1,2) and C (3,1) . Find the coordinates of the image after a dilation with respect to the origin using a scale factor of 2 and then a translation 2 units left and 1 unit up.

Answer 1

Answer:

See below ~

Step-by-step explanation:

Dilation of points with scale factor of 2 :

⇒ A = 2(2, 5) = (4, 10)

⇒ B = 2(1, 2) = (2, 4)

⇒ C = 2(3, 1) = (6, 2)

Translation 2 units left :

⇒ A' = (4 - 2, 10) = (2, 10)

⇒ B' = (2 - 2, 4) = (0, 4)

⇒ C' = (6 - 2, 2) = (4, 2)

Translation 1 unit up :

⇒ A" = (2, 10 + 1) = (2, 11)

⇒ B" = (0, 4 + 1) = (0, 5)

⇒ C" = (4, 2 + 1) = (4, 3)

Answer 2

K=2

• A'=2(2.5)=(4,10)
• B'=2(1,2)=(2,4)
• C'=2(3,1)=(6,2)

Translation of 2 units left means change in x

• A''=(4-2,10)=(2,10)
• B"=(2-2,4)=(0,4)
• C"=(6-2,2)=(4,2)

Translation of 1 units up means change in y

• A'''=(2,10+1)=(2,11)
• B'''=(0,4+1)=(0,5)
• C'''=(4,2+1)=(4,3)