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The vertices of triangle ABC are A(11,3), B(2k, k) and C(-1,-11).
(a) Find the two possible values of k if angle ABC is 90°.
(b) Draw the diagrams to show the two possible triangles.
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How the problem is posed/worded/formulated in the post,
its educational meaning disappeared, in full.
Meanwhile, the meaning can be restored and problem can be nicely presented
as a nice problem, if to re-formulate it in a right way.
This right way to re-formulate is as follows:
The vertices of triangle ABC are A(11,3), B(2k, k) and C(-1,-11).
How to construct geometrically the point B (two possible positions)
in a way that the triangle ABC be a right-angled triangle with the right angle at B ?
Then the answer (the geometric construction) is as follows:
(a) draw a circle with the diameter AC;
(b) then draw the straight line y = .
(c) Two intersection points of the line with the circle will give
two possible positions/locations of the vertex B.