If the medians AD and BE of the triangle with vertices $A (0, b), B (0, 0)$ and $C (a, 0)$ are perpendicular,
then an equation of the line through (a, b) perpendicular to AC is

Question

If the medians AD and BE of the triangle with vertices $$A(0$$, $$b)$$, B (0$$, $$0) and C (a$$, $$0) are perpendicular,then an equation of the line through (a$$, $$b) perpendicular to AC is

Infinity Learn · Accepted Answer

Slope of AD $$=b$$−$$00$$−$$a/2=$$−$$2baSlope$$ of $$BE=b/2a/2=baSince$$ AD and BE are perpendicular −$$2ba$$⋅$$ba=$$−$$1$$ ⇒ $$a2=2b2$$               (i)  Slope of AC is – $$b/a$$ ∴ Equation of the line through (a$$, $$b) perpendicular to AC isy−$$b=cb(x$$−$$a)$$⇒ ax−$$by=a2$$−$$b2$$⇒±$$2bx$$−$$by=b2$$ from (i)±$$2x$$−$$y=b$$ ⇒ $$y=$$±$$2x$$−bSo an equation of required line is $$y=2x$$−b

If the medians AD and BE of the triangle with vertices $A (0, b), B (0, 0)$ and $C (a, 0)$ are perpendicular,
then an equation of the line through (a, b) perpendicular to AC is

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If the medians AD and BE of the triangle with vertices A(0, b), B (0, 0) and C (a, 0) are perpendicular,then an equation of the line through (a, b) perpendicular to AC is

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

If the medians AD and BE of the triangle with vertices $A (0, b), B (0, 0)$ and $C (a, 0)$ are perpendicular,
then an equation of the line through (a, b) perpendicular to AC is