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Question

The vertices of ▲ A(2,-3), B(5,-5) and C(3,0). ▲ ABC is translated through vector (2,-3)' to get the image ▲A'B'C' and ▲A'B'C is rotated through quarter turn in anticlockwise direction about origin to get image ▲A"B''C''. Find the coordinates of the vertices of ▲A'B'C and ▲A''B''C'' and plot it in graph?

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Answer 1 · 2018-03-23T06:28:34

The vertices of #∆A''B''C''# are
#A''(9, 4), B''(8, 7) and C''(3, 5)#.

Warning : Long answer

The vertices of #∆ABC# are #A(2, -3), B(5, -5) and C(3, 0)#.

Translation vector #= (2, -3)#

When the translation vector, #T =(a, b)# then,

#P(x, y) ⟶ P'(x+a, y+b)#

# A(2, -3) ⟶ A'{2 + 2, -3 + (-3)} = A'(4, -9)#
# B(5, -5) ⟶ B'{5 + 2, -5 + (-3)} = B'(7, -8)#
# C(3, 0) ⟶ C'{3 +2, 0 + (-3)} = C'(5, -3)#

The vertices of #∆A'B'C'# are #A'(4, -9), B'(7, -8) and C'(5, -3)#

Under rotation about origin through quarter turn in anticlockwise direction #(+90^0)#,

#P(x, y) → P'(-y,x)#

# A'(4, -9) → A''(9, 4)#
#B'(7, -8) → B''(8, 7)#
#C'(5, -3) → C''(3, 5)#
The vertices of #∆A''B''C''# are
#A''(9, 4), B''(8, 7) and C''(3, 5)#.

enter image source here

Here, yellow colored triangle represents #∆ABC# with vertices #A(2, -3), B(5, -5) and C(3, 0)#.

Red colored triangle represents #∆A'B'C'# with vertices #A'(4, -9), B'(7, -8) and C'(5, -3)#.

Blue colored triangle represents #∆A''B''C''# with vertices #A''(9, 4), B''(8, 7) and C''(3, 5)#.

Hope it helps :)