(B) Let the point be $P(k, k)$.Since $P$ is equidistant from $A(1, 0)$ and $B(0, 3)$,we have $PA = PB$.Using the distance formula,$PA^2 = PB^2$:$(k -

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(B) Let the point be $P(k, k)$.Since $P$ is equidistant from $A(1, 0)$ and $B(0, 3)$,we have $PA = PB$.Using the distance formula,$PA^2 = PB^2$:$(k - 1)^2 + (k - 0)^2 = (k - 0)^2 + (k - 3)^2$$(k^2 - 2k + 1) + k^2 = k^2 + (k^2 - 6k + 9)$$2k^2 - 2k + 1 = 2k^2 - 6k + 9$$-2k + 1 = -6k + 9$$4k = 8$$k = 2$Thus,the point is $(2, 2)$.

Class 11 Mathematics Straight Line System of co-ordinates, Distance between two points, Section formulae

Easy

Find a point whose $x$-coordinate and $y$-coordinate are equal,and which is equidistant from the points $A(1, 0)$ and $B(0, 3)$.

A
$(3, 3)$
B
$(2, 2)$
C
$(1, 1)$
D
$(4, 4)$

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Straight Line

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System of co-ordinates, Distance between two points, Section formulae

If the distance between the points $(a \cos \theta, a \sin \theta)$ and $(a \cos \phi, a \sin \phi)$ is $2a$,then $\theta$ is equal to

EasyTS EAMCET 2004

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The line $x + y = 4$ divides the line segment joining the points $(-1, 1)$ and $(5, 7)$ in the ratio:

EasyIIT 1965

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Find the slope of a line,which passes through the origin and the mid-point of the line segment joining the points $P(0, -4)$ and $B(8, 0)$.

Medium

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If the line segment joining the points $(0, 0)$ and $(3, 4)$ is the hypotenuse of a right-angled triangle,what is the length of the median to the hypotenuse?

Difficult

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If the polar coordinates of a point are $\left(2, \frac{\pi}{4}\right)$,then its Cartesian coordinates are

MediumMHT CET 2021

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Find a point whose $x$-coordinate and $y$-coordinate are equal,and which is equidistant from the points $A(1, 0)$ and $B(0, 3)$.

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If the distance between the points $(a \cos \theta, a \sin \theta)$ and $(a \cos \phi, a \sin \phi)$ is $2a$,then $\theta$ is equal to

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