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A line passes through (x1,y1)and (h , k...

A line passes through `(x_1,y_1)`and `(h , k)`. If slope of the line is m, show that `k-y_1=m(h-x_1)`.

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The slope of the line passing through `( x_1, y_1)` and (h,k) is ` (k-y_1) div (h-x_1)`
It is given that the slope of the line is m.
` (k-y_1) div (h-x_1)=m`
`k-y_1=m (h -x_1)` ...
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Knowledge Check

  • If a line passing through (4, 1, 2) and (5, k, 0) is perpendicular to the line passing through (2, 1, 1) and (3, 3, -1), then k =

    A
    `(1)/(2)`
    B
    `(-1)/(2)`
    C
    `(3)/(2)`
    D
    `(-3)/(2)`

  • What is the equation of the plane passing through (x_1,y_1,z_1) and normal to the line with lt a, b, c gt as firection ratios ?

    A
    `ax+by+cz=ax_1+by_1+cz_1`
    B
    `a(x+x_1)+b(y+y_1)+c(z+z_1)=0`
    C
    `ax+by+cz=0`
    D
    `ax+by+cz=x_1+y_1+z_1=0`

  • Joint equation of lines passing through the origin, and parallel to the lines y-m_(1)x+c_(1) and y=m_(1)x+c_(2) , is

    A
    `m_(1)m_(2)x^(2)-(m_(1)_m_(2))xy+y^(2)=0`
    B
    `m_(1)m_(2)x^(2)+(m_(1)+m_(2))xy+y^(2)=0`
    C
    `m_(1)m_(2)y^(2)-(m_(1)+m_(2))xy+x^(2)=0`
    D
    `m_(1)m_(2)y^(2)+(m_(1)+m_(2))xy+x^(2)=0`