If Q 0-1 is equidistant from P 5-3 and R x - 6- find the value of x-A- x-4B- x-4C- x-5D- x-5

The correct options are A x = 4 B x = 4PQ = QR √((5 0)^2+( 3 1)^2)=√((0 x)^2+(1 6)^2) √((5)^2+( 4)^2)=√(( x)^2+( 5)^2) √(25+16)=√(x^2+25) 41 = x^2 + 25 16 = x^ ...

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Byju's Answer

Standard IX

Mathematics

Betweenness

If Q 0,1 is e...

Question

If Q (0, 1) is equidistant from P (5, - 3) and R (x, 6), find the value of x.

x = 4

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x = -4

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x = 5

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x = -5

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Solution

The correct options are
A x = 4
B x = -4
PQ = QR
$\sqrt{(5 - 0)^{2} + (- 3 - 1)^{2}} = \sqrt{(0 - x)^{2} + (1 - 6)^{2}}$
$\sqrt{(5)^{2} + (- 4)^{2}} = \sqrt{(- x)^{2} + (- 5)^{2}}$
$\sqrt{25 + 16} = \sqrt{x^{2} + 25}$
$41 = x^{2} + 25$
$16 = x^{2}$
$x = \pm 4$
Therefore, point R is (4, 6) or ( - 4, 6).

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If Q (0, 1) is equidistant from P (5, - 3) and R (x, 6), find the value of x.

The correct options are A x = 4 B x = -4PQ = QR √(5−0)2+(−3−1)2=√(0−x)2+(1−6)2 √(5)2+(−4)2=√(−x)2+(−5)2 √25+16=√x2+25 41=x2+25 16=x2 x=±4 Therefore, point R is (4, 6) or ( - 4, 6).