(B) Let the point $P(8, 4)$ divide the line segment joining $A(5, -2)$ and $B(9, 6)$ in the ratio $k : 1$.Using the section formula,the coordinates of

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(B) Let the point $P(8, 4)$ divide the line segment joining $A(5, -2)$ and $B(9, 6)$ in the ratio $k : 1$.Using the section formula,the coordinates of $P$ are given by:$P = \left( \frac{k(9) + 1(5)}{k + 1}, \frac{k(6) + 1(-2)}{k + 1} \right)$Equating the $x$-coordinate:$8 = \frac{9k + 5}{k + 1}$$8(k + 1) = 9k + 5$$8k + 8 = 9k + 5$$8 - 5 = 9k - 8k$$k = 3$Thus,the ratio $k : 1$ is $3 : 1$.

Class 11 Mathematics Straight Line System of co-ordinates, Distance between two points, Section formulae

Easy

In what ratio does the point $(8, 4)$ divide the line segment joining the points $(5, -2)$ and $(9, 6)$?

A
$2 : 1$
B
$3 : 1$
C
$2 : 3$
D
$1 : 2$

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Class 11

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Chapter

Straight Line

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System of co-ordinates, Distance between two points, Section formulae

Find the distance between $P(x_{1}, y_{1})$ and $Q(x_{2}, y_{2})$ when $PQ$ is parallel to the $y$-axis.

Easy

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Find the distance between the points $P \left( 3, -\frac{\pi}{6} \right)$ and $Q \left( 4, \frac{\pi}{3} \right)$ in polar coordinates.

Medium

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Find a point whose $x$-coordinate and $y$-coordinate are equal,and which is equidistant from the points $A(1, 0)$ and $B(0, 3)$.

Easy

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Find the coordinates of the point that divides the line segment joining the points $(3, -1)$ and $(3, 4)$ externally in the ratio $2 : 3$.

Easy

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In what ratio does the line $3x + 4y = 7$ divide the line segment joining the points $(1, 2)$ and $(-2, 1)$?

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In what ratio does the point $(8, 4)$ divide the line segment joining the points $(5, -2)$ and $(9, 6)$?

Similar Questions

Find the distance between $P(x_{1}, y_{1})$ and $Q(x_{2}, y_{2})$ when $PQ$ is parallel to the $y$-axis.

Find the distance between the points $P \left( 3, -\frac{\pi}{6} \right)$ and $Q \left( 4, \frac{\pi}{3} \right)$ in polar coordinates.

Find a point whose $x$-coordinate and $y$-coordinate are equal,and which is equidistant from the points $A(1, 0)$ and $B(0, 3)$.

Find the coordinates of the point that divides the line segment joining the points $(3, -1)$ and $(3, 4)$ externally in the ratio $2 : 3$.

In what ratio does the line $3x + 4y = 7$ divide the line segment joining the points $(1, 2)$ and $(-2, 1)$?

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