Question

Distance of the point P(x, y) from x-axis is ly and from y-axis is x
Problems:
Find the distance between the points (3,2) and (1,1).
If the distance between the points (k: 2) and (3.4) is 8 then the value of k.
Find the distance of the point (x.y) from its image in x-axis.
The number of points equidistant from two given points.
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If (2.1). (2.5) are opposite corners of a square then the length of its side is.
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A (5.3), B(11.-5), P(12.2) are three points. If APB = 90° then value of is.
nt of division:​

Answer 1

Answer:

1.Find the distance between the points (3,2) and (1,1).

2.If the distance between the points

(k,2) and (3,4) is 8 

Formula used:

The distance between two points $(x_1,y_1)\:and\:(x_2,y_2)\:is\:d= \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

1.

Given points are (3,2) and (1,1)

$d= \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

$d= \sqrt{(3-1)^2+(2-1)^2}$

$d= \sqrt{(2)^2+(1)^2}$

$d= \sqrt{4+1}$

$d= \sqrt{5}\:units$

2.

Given:

Distance between (k,2) and (3,4) is 8

$\implies\:\sqrt{(k-3)^2+(2-4)^2}=8$

squaring on both sides

$(k-3)^2+4=64$

$(k-3)^2=64-4$

$(k-3)^2=60$

$k-3$=±$\sqrt{60}$

$k$=3±$2\sqrt{15}$