question related to right triangle

Question

Plot the points A(-5, 0) and B(-2, -3). C is a point such that triangle ABC is a right triangle. Find all possible positions for C. Write the coordinates of each point.

i found 2

1) C (-2,0)

2) C(-5,-3)

please tell me others and explain too

Answer 1

There are an infinite number of places for C, if any of the three angles can be a right angle. If A or B are right angles all the points for C lie on the line y=x+5 or y=x-1, which are parallel to one another.

I've added 4 more points as examples. Also, if you draw a circle (centre (-3.5,-1.5)) with AB as the diameter, any point on the circumference will be a right angle, so C can be anywhere on the circumference. The equation of the circle is (x+3.5)^2+(y+1.5)^2=4.5 or (2x+7)^2+(2y+3)^2=18.

Comments

thanx . please check my last answer too (reflection and translation ) i made tessellation again , did i make correct or not plz do confirm me . thank u

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Please see my comment on the tesselation question.

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A further comment on the placing of point C in this question is to draw the figure with points A and B marked, but no points C, just leaving the two parallel lines and circle to indicate all the possible places where C could be placed (that is, on the lines or on the circumference of the circle).