COMEDK · Maths · 10. Straight Lines

If two vertices of a triangle are \((3,-2)\) and \((-2,3)\) and its orthocentre is \((-6,1)\).
Then the difference between ordinate and abscissa of the third vertex of the triangle is

A \(2\)
B \(-5\)
C \(7\)
D \(5\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(7\)

Step-by-step Solution

Detailed explanation

Let the vertices of the triangle be \(A(3, -2)\), \(B(-2, 3)\), and \(C(x, y)\). The orthocentre \(H\) is given as \((-6, 1)\). The slope of \(BC\) is \(m_{BC} = \dfrac{y - 3}{x - (-2)} = \dfrac{y - 3}{x + 2}\). Since \(AH \perp BC\), the slope of \(AH\) is…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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If two vertices of a triangle are \((3,-2)\) and \((-2,3)\) and its orthocentre is \((-6,1)\).Then the difference between ordinate and abscissa of the third vertex of the triangle is

Step-by-step Solution

If two vertices of a triangle are \((3,-2)\) and \((-2,3)\) and its orthocentre is \((-6,1)\).
Then the difference between ordinate and abscissa of the third vertex of the triangle is