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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 :)