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in Co-ordinate geometry by (52.7k points)

The straight lines 3x + 4y = 5 and 4x − 3y = 15 intersect at the point A. On these lines the points B and C are chosen so that AB = AC. Find the possible equations of the line BC passing through (1, 2).

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Two straight lines are given at right angles. Since AB = AC, the triangle is an isosceles right-angled triangle. The required equation is of the form

y – 2 = m(x – 1)  .....(1)

Substituting the value of m in Eq. (1), we get the required equations. Equation of lines are y – 2 = –7 (x – 1) and y - 2 = 1/7 (x - 1).

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