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प्रश्न
Show that lines x − 2y − 7 = 0 and 2x + y + 1 = 0 are perpendicular to each other. Find their point of intersection
उत्तर
Slope of the line x − 2y − 7 = 0 is
m1 = `-"coefficient of x"/"coefficient of y" = -1/((-2)) = 1/2`
Slope of the line 2x + y + 1 = 0 is
m2 = `-"coefficient of x"/"coefficient of y" = -2/1` = − 2
Since m1 = m2 = `1/2(-2)` = − 1 the lines are perpendicular to each other.
To find the point of intersection, we have to solve
x − 2y − 7 = 0 ...(1)
and 2x + y + 1 = 0 ...(2)
Multiplying equation (2) by 2, we get
4x + 2y + 2 = 0 ...(3)
Adding equations (1) and (3), we get
5x − 5 = 0
∴ x = 1
∴ from (2), 2(1) + y + 1 = 0
∴ y = −3
Hence, the point of intersection of the lines is (1, −3).
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