(D) The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = d$. Given points are $(a, 2)$ an

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(D) The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} = d$. Given points are $(a, 2)$ and $(3, 4)$ with distance $d = 8$. So,$\sqrt{(3 - a)^2 + (4 - 2)^2} = 8$. Squaring both sides,we get $(3 - a)^2 + (2)^2 = 8^2$. $(3 - a)^2 + 4 = 64$. $(3 - a)^2 = 60$. $3 - a = \pm \sqrt{60} = \pm 2\sqrt{15}$. $a = 3 \pm 2\sqrt{15}$.

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

Difficult

If the distance between the points $(a, 2)$ and $(3, 4)$ is $8$,then $a = $

A
$2 + 3\sqrt{15}$
B
$2 - 3\sqrt{15}$
C
$2 \pm 3\sqrt{15}$
D
$3 \pm 2\sqrt{15}$

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Class 11

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Chapter

Straight Lines

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

Find the points of trisection of the line segment joining the points $A(2, 1)$ and $B(5, 3)$.

Medium

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

Easy

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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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What is the square root of the sum of the squares of the lengths of the perpendiculars drawn from the point $(-3, 4)$ to both axes?

Easy

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Find the coordinates of the point which divides the line segment joining the points $(a + b, a - b)$ and $(a - b, a + b)$ externally in the ratio $a : b$.

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If the distance between the points $(a, 2)$ and $(3, 4)$ is $8$,then $a = $

Similar Questions

Find the points of trisection of the line segment joining the points $A(2, 1)$ and $B(5, 3)$.

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

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

What is the square root of the sum of the squares of the lengths of the perpendiculars drawn from the point $(-3, 4)$ to both axes?

Find the coordinates of the point which divides the line segment joining the points $(a + b, a - b)$ and $(a - b, a + b)$ externally in the ratio $a : b$.

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