Excuse me, do you know rotations?

Geometry Level 3

There are points $A(1, 1)$ , $B(5, 9)$ and $C(2, 3)$ . Also, there is an ambigious point $R$ with unknown coordinates. A rotation is performed, with $R$ as centre of the rotation. It is known that $A'$ , $B'$ and $C'$ are points $A$ , $B$ and $C$ , respectively, after rotation. It is also known that $A'(3, -5)$ and $B'(11, -9)$ . Calculate the are of triangle $ABC'$

The answer is 30.

1 solution

Milan Milanic
Jan 9, 2016

Solution:

Segment $AB$ is rotated, and with it, all points that belong to that segment. Point $C$ , also belongs to that segment and it can be concluded that $AC:BC = 1:3$ . Therefore, coordinates of $C$ can be calculated through formula $C(\frac { 3X_{ A } + { X }_{ B } }{ 4 } ,\frac { 3{ Y }_{ A } + { Y }_{ B } }{ 4 } )$ . This can be reused with points $A'$ and $B'$ , then we get that $C'(5, -6)$

Now, we have coordinates of all crucial points for calculating area of triangle $ABC'$ and we easily can find that its area is $30$ .

i did it the same way.

aryan goyat - 5 years, 5 months ago

Excuse me, do you know rotations?

The answer is 30.

1 solution

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