(C) The distance formula between two points $(x_1, y_1)$ and $(x_2, y_2)$ is $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.Given points are $(x, 2)$ and

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(C) The distance formula between two points $(x_1, y_1)$ and $(x_2, y_2)$ is $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.Given points are $(x, 2)$ and $(3, 4)$ with distance $d = 2$.Substituting the values: $2 = \sqrt{(x - 3)^2 + (2 - 4)^2}$.$2 = \sqrt{(x - 3)^2 + (-2)^2}$.$2 = \sqrt{(x - 3)^2 + 4}$.Squaring both sides: $4 = (x - 3)^2 + 4$.$(x - 3)^2 = 0$.$x - 3 = 0$.$x = 3$.

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

Easy

If the distance between the points $(x, 2)$ and $(3, 4)$ is $2$,find the value of $x$.

A
$1$
B
$2$
C
$3$
D
$0$

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

Find the distance between the points $P(-2, 3)$ and $Q(4, -1)$.

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

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In what ratio does the $x$-axis divide the line segment joining the points $(3, -4)$ and $(-5, 6)$?

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If the distance between the points $(x, 2)$ and $(3, 4)$ is $2$,find the value of $x$.

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Find the distance between the points $P(-2, 3)$ and $Q(4, -1)$.

The line segment joining the points $(2, -3)$ and $(-5, 6)$ is divided by the $y$-axis in the ratio:

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

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