(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 $A(-4, -3)$ and $B(6, a)

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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 $A(-4, -3)$ and $B(6, a)$ with distance $d = 10$.$10 = \sqrt{(6 - (-4))^2 + (a - (-3))^2}$$10 = \sqrt{(10)^2 + (a + 3)^2}$Squaring both sides:$100 = 100 + (a + 3)^2$$(a + 3)^2 = 0$$a + 3 = 0$$a = -3$

Class 10 Mathematics Coordinate Geometry Mix Examples - Coordinate Geometry

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If the distance between $A(-4, -3)$ and $B(6, a)$ is $10$,then $a = \ldots \ldots \ldots . . .$

A
$4$
B
$3$
C
$-3$
D
$-4$

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$AOBC$ is a rectangle whose three vertices are $A (0, 3)$,$O (0, 0)$,and $B (5, 0)$. The length of its diagonal is

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If the point $P (2,1)$ lies on the line segment joining points $A (4,2)$ and $B (8,4)$,then:

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The coordinates of the midpoint of the line segment joining the points $(20, 10)$ and $(6, 8)$ are:

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The coordinates of the point dividing the line segment joining $A(2, 1)$ and $B(-2, -1)$ in the ratio $1:1$ from $A$ are ..............

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If the distance between $A(1, 3)$ and $B(a, 0)$ is $3$ units,then $a = \ldots$

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If the distance between $A(-4, -3)$ and $B(6, a)$ is $10$,then $a = \ldots \ldots \ldots . . .$

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$AOBC$ is a rectangle whose three vertices are $A (0, 3)$,$O (0, 0)$,and $B (5, 0)$. The length of its diagonal is

If the point $P (2,1)$ lies on the line segment joining points $A (4,2)$ and $B (8,4)$,then:

The coordinates of the midpoint of the line segment joining the points $(20, 10)$ and $(6, 8)$ are:

The coordinates of the point dividing the line segment joining $A(2, 1)$ and $B(-2, -1)$ in the ratio $1:1$ from $A$ are ..............

If the distance between $A(1, 3)$ and $B(a, 0)$ is $3$ units,then $a = \ldots$

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