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प्रश्न
The equation of the straight line passing through the point (3, 2) and perpendicular to the line y = x is ______.
पर्याय
x – y = 5
x + y = 5
x + y = 1
x – y = 1
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उत्तर
The equation of the straight line passing through the point (3, 2) and perpendicular to the line y = x is x + y = 5.
Explanation:
Equation of line ‘l’ is given by y – y1 = m(x – x1).
Since l passing through the point P(3, 2).
∴ y – 2 = m(x – 3)
⇒ y = mx + 2 – 3m .....(i)
Since it is given that lines y = x
And ‘l’ are perpendicular to each other
∴ `"m" xx1`= –1 .....`[because "m"_1 xx "m"_2 = - 1]`
m = –1
Put m = – 1 in eqn. (i), we get
y = –x + 2 – 3(–1)
y = –x + 5
x + y = 5
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| Column C1 | Column C2 |
| (a) Through the point (2, 1) is | (i) 2x – y = 4 |
| (b) Perpendicular to the line (ii) x + y – 5 = 0 x + 2y + 1 = 0 is |
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(iii) x – y –1 = 0 |
| (d) Equally inclined to the axes is | (iv) 3x – 4y – 1 = 0 |
