On a graph paper plot the points A(2,-6), B(4,7) and C(-4,4). Then the point of intersection of the locus of a point equidistant from A and B and the locus of a point equidistant from AB and AC lies on the x-axis.
On a graph paper plot the points A(2,-6), B(4,7) and C(-4,4). Then the point of intersection of the locus of a point equidistant from A and B and the locus of a point equidistant from AB and AC lies on the x-axis.
The correct option is B False
Plot the points A(2,-6), B(4,7) and C(-4,4) on a graph paper.
We know that the locus of a point which is equidistant from two fixed points is the perpendicular bisector of the line segment joining the two fixed points.
Hence to find the locus of a point equidistant from A and B, we draw a perpendicular bisector 'm' of AB, a shown above.
Also, we know that the locus of a point equidistant from two intersecting straight lines is a pair of straight lines which bisect the angles between the given lines.
Hence to find the locus of a point equidistant from AB and AC, we draw the angle bisector 'l' of angle A.
From these constructions, we note that the lines 'l' and 'm' intersect at a point(P, in the graph) which lies in the first quadrant.
Hence the given statement is false.
False
Plot the points A(2,-6), B(4,7) and C(-4,4) on a graph paper.
We know that the locus of a point which is equidistant from two fixed points is the perpendicular bisector of the line segment joining the two fixed points.
Hence to find the locus of a point equidistant from A and B, we draw a perpendicular bisector 'm' of AB, a shown above.
Also, we know that the locus of a point equidistant from two intersecting straight lines is a pair of straight lines which bisect the angles between the given lines.
Hence to find the locus of a point equidistant from AB and AC, we draw the angle bisector 'l' of angle A.
From these constructions, we note that the lines 'l' and 'm' intersect at a point(P, in the graph) which lies in the first quadrant.
Hence the given statement is false.
