If the locus of a point which is equidistant | vedclass

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(B) The locus of a point $(x, y)$ equidistant from the coordinate axes is given by $|x| = |y|$,which implies $y = x$ or $y = -x$.These two lines inter

Vedclass · Accepted Answer

$9$

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(B) The locus of a point $(x, y)$ equidistant from the coordinate axes is given by $|x| = |y|$,which implies $y = x$ or $y = -x$.These two lines intersect at the origin $(0, 0)$.The line $y = 3$ intersects $y = x$ at $(3, 3)$ and $y = -x$ at $(-3, 3)$.These three lines form a triangle with vertices at $(0, 0)$,$(3, 3)$,and $(-3, 3)$.The base of this triangle lies on the line $y = 3$ and its length is the distance between $(-3, 3)$ and $(3, 3)$,which is $|3 - (-3)| = 6$.The height of the triangle is the perpendicular distance from the origin $(0, 0)$ to the line $y = 3$,which is $3$.The area of the triangle is $\frac{1}{2} 	imes 	ext{base} 	imes 	ext{height} = \frac{1}{2} 	imes 6 	imes 3 = 9$.

If the locus of a point which is equidistant from the coordinate axes forms a triangle with the line $y=3$,then the area of the triangle is

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