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Question
Find the slope of a line, which passes through the origin, and the mid-point of the line segment joining the points P (0, –4) and B (8, 0).
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Solution
Mid point of the line segment joining the points P(0, –4) and B(8, 0)
`"x" = ("x"_1 + "x"_2)/2`
= `(0 + 8)/2`
= 4
y = `("y"_1 + "y"_2)/2`
= `(-4 + 0)/2`
= `(-4)/2`
= −2
= The midpoint of PB has coordinates (4, −2) of M.
The coordinates of the origin point 0 are (0, 0).
∴ OM = `("y"_2 - "y"_1)/("x"_2 - "x"_1)`
= `(-2 -0)/(4 - 0)`
= `(-2)/4`
= `(-1)/2`
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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 |
(ii) x + y – 5 = 0 |
| (c) Parallel to the line (iii) x – y –1 = 0 3x – 4y + 5 = 0 is |
(iii) x – y –1 = 0 |
| (d) Equally inclined to the axes is | (iv) 3x – 4y – 1 = 0 |
