Points are in confusion
Algebra
Level
2
The points (-a, -b), (0, 0), (a, b) and (a*a, ab) are?
vertices of paralleleogram
vertices of rectangle
Collinear
vertices of a rhombus
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1 solution
(-a, -b), (0, 0), (a, b) are all collinear because (-a,-b) is a reflection over y = x of (a,b). Finding the slope between the two unknown points gives us slope = b/a. Therefore, the equation of the line is (y-b)=b/a(x-a). Plugging in (a*a,ab) shows that the point does indeed lie on the equation.