(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

Medium

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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Show that,for every $a \in R$,the area of the triangle having the vertices $A(5, a)$,$B(2, 5)$,and $C(2, 3)$ is $3$ square units.

Medium

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State whether the following statements are true or false. Justify your answer.
The points $(0,5), (0,-9)$ and $(3,6)$ are collinear.

Medium

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Show that the points $A(2, 2)$,$B(-2, 2)$,$C(-2, -2)$,and $D(2, -2)$ are the vertices of a square.

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Find the values of $k$ if the points $A(k+1, 2k)$,$B(3k, 2k+3)$ and $C(5k-1, 5k)$ are collinear.

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If the vertices of $\Delta ABC$ are $A(9,5), B(6,7)$ and $C(3,3)$,then the length of median $\overline{BE}$ is.......

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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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Show that,for every $a \in R$,the area of the triangle having the vertices $A(5, a)$,$B(2, 5)$,and $C(2, 3)$ is $3$ square units.

State whether the following statements are true or false. Justify your answer.The points $(0,5), (0,-9)$ and $(3,6)$ are collinear.

Show that the points $A(2, 2)$,$B(-2, 2)$,$C(-2, -2)$,and $D(2, -2)$ are the vertices of a square.

Find the values of $k$ if the points $A(k+1, 2k)$,$B(3k, 2k+3)$ and $C(5k-1, 5k)$ are collinear.

If the vertices of $\Delta ABC$ are $A(9,5), B(6,7)$ and $C(3,3)$,then the length of median $\overline{BE}$ is.......

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State whether the following statements are true or false. Justify your answer.
The points $(0,5), (0,-9)$ and $(3,6)$ are collinear.