Straight Lines · JEE Preparation Mathematics
Find the equation of the line that passes through the point of intersection of 2x + 3y - 7 = 0 and x - y + 1 = 0, and is perpendicular to x + 2y - 5…
Practice question from Straight Lines (JEE Preparation Mathematics), with the correct answer and a step-by-step solution.
medium · Subjective · Q-4B1111
Find the equation of the line that passes through the point of intersection of 2x + 3y - 7 = 0 and x - y + 1 = 0, and is perpendicular to x + 2y - 5 = 0.
Answer: The two given lines intersect at (4/5, 9/5). The line x + 2y - 5 = 0 has slope -1/2, so the required perpendicular line has slope 2. Therefore, its equation is y - 9/5 = 2(x - 4/5), or 10x - 5y + 1 = 0.
Solution
Solving and gives . The slope of is , so the required perpendicular slope is . Hence, , or .
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