The coordinates of a point at a distance -5 from the point 3- 4 and having the same abcissa and ordinate are

The correct options are B (5,5) C (2,2) Distance of point from (3,4) is √(5) and abcissa and ordinate is same then let say x=y=a. No ...

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Standard X

Mathematics

Distance between Two Points on the Same Coordinate Axes

The coordinat...

Question

The coordinates of a point at a distance $\sqrt{5}$ from the point $(3, 4)$ and having the same abcissa and ordinate are

(2, 2)

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(- 2, - 2)

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(5, 5)

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(- 5, - 5)

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Solution

The correct options are
B $(5, 5)$
C $(2, 2)$
Distance of point from $(3, 4)$ is $\sqrt{5}$ and abcissa and ordinate is same then let say $x = y = a .$
Now using distance formula, we have
$\sqrt{{(a - 3)}^{2} + {(a - 4)}^{2}} = \sqrt{5}$
${(a - 3)}^{2} + {(a - 4)}^{2} = 5$
$a^{2} + 9 - 6 a + a^{2} + 16 - 8 a = 5$
$2 a^{2} - 14 a + 20 = 0$
$a^{2} - 7 a + 10 = 0$
$(a - 5) (a - 2) = 0$
$a = 5$ and $2$
Points are $(2, 2)$ and $(5, 5) .$

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The coordinates of a point at a distance √5 from the point (3,4) and having the same abcissa and ordinate are

The coordinates of a point at a distance $\sqrt{5}$ from the point $(3, 4)$ and having the same abcissa and ordinate are