(A) Given $AB = BC$,we use the distance formula: $\sqrt{(6-1)^2 + (-1-3)^2} = \sqrt{(x-1)^2 + (8-3)^2}$.Squaring both sides: $(5)^2 + (-4)^2 = (x-1)^2

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(A) Given $AB = BC$,we use the distance formula: $\sqrt{(6-1)^2 + (-1-3)^2} = \sqrt{(x-1)^2 + (8-3)^2}$.Squaring both sides: $(5)^2 + (-4)^2 = (x-1)^2 + (5)^2$.$25 + 16 = (x-1)^2 + 25$.$16 = (x-1)^2$.Taking the square root: $x-1 = \pm 4$.Case $1$: $x-1 = 4 \Rightarrow x = 5$.Case $2$: $x-1 = -4 \Rightarrow x = -3$.Therefore,$x = 5, -3$.

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

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If the points $A(6, -1)$,$B(1, 3)$ and $C(x, 8)$ are such that $AB = BC$,then $x = $

A
$-3, 5$
B
$3, -5$
C
$-3, -5$
D
$3, 5$

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Straight Line

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

The coordinates of a point are $(0, 1)$ and the ordinate of another point is $-3$. If the distance between the two points is $5$,then the abscissa of the other point is:

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If the distance between the points $(a \cos \theta, a \sin \theta)$ and $(a \cos \phi, a \sin \phi)$ is $2a$,then $\theta$ is equal to

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

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What are the coordinates of the point that divides the line segment joining the points $(-3, -4)$ and $(-8, 7)$ externally in the ratio $7 : 5$?

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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 points $A(6, -1)$,$B(1, 3)$ and $C(x, 8)$ are such that $AB = BC$,then $x = $

Similar Questions

The coordinates of a point are $(0, 1)$ and the ordinate of another point is $-3$. If the distance between the two points is $5$,then the abscissa of the other point is:

If the distance between the points $(a \cos \theta, a \sin \theta)$ and $(a \cos \phi, a \sin \phi)$ is $2a$,then $\theta$ is equal to

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

What are the coordinates of the point that divides the line segment joining the points $(-3, -4)$ and $(-8, 7)$ externally in the ratio $7 : 5$?

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

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