(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

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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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Straight Line

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

If the midpoint of the line segment joining the points $(5, a)$ and $(b, 7)$ is $(3, 5)$,find $(a, b)$.

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If $C$ is the reflection of $A(2, 4)$ in the $x$-axis and $B$ is the reflection of $C$ in the $y$-axis, then $|AB|$ is

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If $A$ and $B$ are the points $(-3, 4)$ and $(2, 1)$,then the coordinates of the point $C$ on $AB$ produced such that $AC = 2 BC$ are:

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

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If the midpoint of the line segment joining the points $(5, a)$ and $(b, 7)$ is $(3, 5)$,find $(a, b)$.

If the coordinates of two opposite vertices of a square are $(a, b)$ and $(b, a)$,find the area of the square.

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