COMEDK · Maths · 10. Straight Lines
In a \(\triangle A B C\), if coordinates of point \(A\) is \((1,2)\) and equation of the medians through \(B\) and \(C\) are \(x+y=5\) and \(x=4\) respectively, then the coordinates of \(B\) is
- A \((1,4)\)
- B \((7,-2)\)
- C (4, 1)
- D \((-2,7)\)
Answer & Solution
Correct Answer
(B) \((7,-2)\)
Step-by-step Solution
Detailed explanation
Let the coordinates of \(A\) be \((1,2)\). Let the median through \(B\) be \(L_1: x+y=5\) and the median through \(C\) be \(L_2: x=4\). The centroid \(G\) is the intersection of the medians \(L_1\) and \(L_2\). Solving \(x+y=5\) and \(x=4\), we get \(4+y=5\), so \(y=1\). Thus,…
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