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On the x-y coordinate grid, are points \(A (x_1, y_1\)) and \(B (x_2, y_2\)) equidistant from the origin?
(1) \(|x_1| = |y_1|\) for point A and \(|x_2| = |y_2|\) for point B
(2) \(|x_1|, |y_1|\) of point A = \(|x_2|, |y_2|\) of point B
@experts I really couldn't understand the explanation for this as below:
(1) \(|x_1| = |y_1|\) for point A and \(|x_2| = |y_2|\) for point B
(2) \(|x_1|, |y_1|\) of point A = \(|x_2|, |y_2|\) of point B
@experts I really couldn't understand the explanation for this as below:
The distance of a point from origin \(\sqrt{x^2 + y^2}\)
Therefore, to find the distance of a point from origin, we only need the absolute values of x and y co-ordinate of a point.
Therefore, to find the distance of a point from origin, we only need the absolute values of x and y co-ordinate of a point.
14 Mar 2020, 11:51
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(1) |x1| = |y1| for point A and |x2| = |y2| for point B --- Implies that x and y coordinates of A are equal , and similarly x and y coordinates of A are equal. Example A(3,3) and B(4,4) . Here A and B are not equidistant from the origin . But A can also be A(2,2) and B (2,2) which would prove that they are equidistant from origin -----Not Suff
(2) |x1|, |y1| of point A = |x2|, |y2| of point B --- Implies that since the coordinates of A and B are same , both the points are actually same. This means that they are at equal distance from origin -----Sufficient
Hence , ans is B
(2) |x1|, |y1| of point A = |x2|, |y2| of point B --- Implies that since the coordinates of A and B are same , both the points are actually same. This means that they are at equal distance from origin -----Sufficient
Hence , ans is B
shameekv1989
14 Mar 2020, 13:06
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Kritisood
Distance of \(x_{1},y_1\) from Origin (0,0) is \(x_{1}^2+ y_1^2\)
Similarly, Distance of \(x_{2},y_2\) from Origin (0,0) is \(x_{2}^2+ y_2^2\)
So we are asked if \(x_{1}^2+ y_1^2\) = \(x_{2}^2+ y_2^2\)?
i) \(|x_1| = |y_1|\) => \(x_{1}^2 = y_1^2\)
\(|x_2| = |y_2|\) => \(x_{2}^2 = y_2^2\)
is \(2x_{1}^2\) = \(2x_{2}^2\) i.e. is \(|x_{1}| = |x_{2}|\)?- We don't know - Insufficient
ii) \(|x_1| = |x_2|\) => \(x_{1}^2 = x_2^2\)
\(|y_1| = |y_2|\) => \(y_{1}^2 = y_2^2\)
is \(x_{1}^2+ y_1^2\) = \(x_{2}^2+ y_2^2\)? => LHS = RHS - Sufficient
Answer - B
