The point whose abscissa is equal to its ordinate and which is eq… - Vidyadip

MCQ

The point whose abscissa is equal to its ordinate and which is equidistant from the points $(1,0)$ and $(0,3)$ is

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

✓

Answer

Correct option: B.

$(2, 2)$

b
(b) Let the point be $(x, x)$, so according to the condition ${(x - 1)^2} + {(x - 0)^2} = {(x - 0)^2} + {(x - 3)^2}$

$ \Rightarrow \,\, - 2x + 1 = - 6x + 9\,\, \Rightarrow \,\,x = 2$.

Hence the point is $(2, 2)$.

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