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Standard XII

Mathematics

Distance Formula

The length of...

Question

The length of line PQ is 10 units and the coordinates of P are $(2, - 3)$ ; calculate the coordinates of point Q, if its abscissa is 10.

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Solution

The length of line pl is 10 units
and the coordinate, p are (2,-3)
;calculate the coordinate of point
l, if abscissa is 10.
$\Rightarrow$ pl = 10 units
$10 = \sqrt{(y - y_{1})^{2} + (x_{2} - x_{1})^{2}}$
$10 = \sqrt{(- 3 - y_{1})^{2} + (2 - 10)^{2}}$
$10^{2} = (3 + y_{1})^{2} + 64$
$(3 + y_{1})^{2} = 100 - 64 = 36$
$3 + y = 6$
$y = 63 = 3$
y = 3
D =( 2,-3) & l = (10,3)

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The length of line PQ is 10 units and the coordinates of P are (2,−3); calculate the coordinates of point Q, if its abscissa is 10.

The length of line pl is 10 unitsand the coordinate, p are (2,-3);calculate the coordinate of pointl, if abscissa is 10.⇒ pl = 10 units10=√(y−y1)2+(x2−x1)210=√(−3−y1)2+(2−10)2102=(3+y1)2+64(3+y1)2=100−64=363+y=6y=63=3y = 3 D =( 2,-3) & l = (10,3)

The length of line PQ is 10 units and the coordinates of P are $(2, - 3)$ ; calculate the coordinates of point Q, if its abscissa is 10.