(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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Class 11 Questions

Class 11

Mathematics Questions

Chapter

Straight Line

Subtopic

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

Find the distance between $P(x_{1}, y_{1})$ and $Q(x_{2}, y_{2})$ when $PQ$ is parallel to the $y$-axis.

Easy

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The distance between the points $(a \cos \alpha, a \sin \alpha)$ and $(a \cos \beta, a \sin \beta)$ is

Easy

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If the line $2x + y = k$ passes through the point which divides the line segment joining the points $(1, 1)$ and $(2, 4)$ internally in the ratio $3:2$,then $(k+1):(k-1) =$

EasyMHT CET 2025

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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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What is the distance of the point $(6, 8)$ from the $x$-axis?

Easy

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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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Find the distance between $P(x_{1}, y_{1})$ and $Q(x_{2}, y_{2})$ when $PQ$ is parallel to the $y$-axis.

The distance between the points $(a \cos \alpha, a \sin \alpha)$ and $(a \cos \beta, a \sin \beta)$ is

If the line $2x + y = k$ passes through the point which divides the line segment joining the points $(1, 1)$ and $(2, 4)$ internally in the ratio $3:2$,then $(k+1):(k-1) =$

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 $B(8, 0)$.

What is the distance of the point $(6, 8)$ from the $x$-axis?

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