In what ratio does the x-y-2=0 divided the line segment joining the points A(3,-1) and B(8,9)?

Solution

let t line x-y-2=0 divid t line segment in t ratio k : 1 at point C
so coordinates of C are

$open parentheses fraction numerator 8 straight k plus 3 over denominator straight k plus 1 end fraction close parentheses comma open parentheses fraction numerator 9 straight k minus 1 over denominator straight k plus 1 end fraction close parentheses$

C lies on x - y - 2 = o

so, subs coordinates of x,y in tis eq.
$open parentheses fraction numerator 8 straight k plus 3 over denominator straight k plus 1 end fraction close parentheses minus open parentheses fraction numerator 9 straight k minus 1 over denominator straight k plus 1 end fraction close parentheses space minus 2 space equals 0 fraction numerator 8 k plus 3 minus 9 k plus 1 minus 2 k minus 2 over denominator k plus 1 end fraction space equals 0 fraction numerator 8 k plus 3 minus 9 k plus 1 minus 2 k minus 2 over denominator k plus 1 end fraction space equals space 0 fraction numerator negative 3 k plus 2 over denominator k plus 1 end fraction space equals space 0 minus 3 k space plus 2 space equals space 0 rightwards double arrow space k space equals space 2 divided by 3 i. e space 2 colon 3$

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Coordinate Geometry

In what ratio does the x-y-2=0 divided the line segment joining the points A(3,-1) and B(8,9)?

Some More Questions From Coordinate Geometry Chapter

Prove that the diagonals of a rectangle ABCD, with vertices A(2, -1), B(5, -1), C(5, 6) and D(2, 6), are equal and bisect each other.

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