On the x-y coordinate grid, are points A(m, n) and B(r, t) equidistant

Question

On the x-y coordinate grid, are points A(m, n) and B(r, t) equidistant from the origin?

(1) |m| = |n| and |r| = |t|
(2) |m| = |r| and |n| = |t|

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On the x-y coordinate grid, are points A and B equidistant from the origin? 
(1) |x| = |y| for point A and |x| = |y| for point B
(2) |x|, |y| of point A = |x|, |y| of point B

IanStewart · Answer

There's a typo in Statement 1; I assume it means to say |m| = |n|, and not "|a| = |b|" (since there is no a or b in the question).

Statement 1 is not sufficient, since it's possible A and B are the same point, and are thus equidistant from the origin, but it's possible A is (1, 1) and B is (1000, 1000) and are at very different distances from the origin.

Statement 2 is sufficient, since if |m| = |r|, then m^2 = r^2, and similarly n^2 = t^2. We use Pythagoras to find the distance from a point to the origin, so the distance from (0, 0) to (m, n) is just √(m^2 + n^2). If m^2 = r^2 and n^2 = t^2, then √(m^2 + n^2) must equal √(r^2 + t^2), the distance from (0, 0) to (r, t).

Bunuel · Answer

__________________
Edited. Thank you.

TestPrepUnlimited · Answer

The distances for A and B to the origin would be  \sqrt{m^2 + n^2}  and  \sqrt{r^2 + t^2} . To have these values equal we must need  m^2 + n^2 = r^2 + t^2 . Then we are asking if this equality is true.

Statement 1: 
We can reduce the question to " 2m^2 = 2r^2 ?" Insufficient.

Statement 2: 
Plug in to get the left side is  r^2 + t^2 , then both sides must be equal. Sufficient.

Ans: B

sambitspm · Answer

See the attachment.
My answer B

bumpbot · Answer

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On the x-y coordinate grid, are points A(m, n) and B(r, t) equidistant

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On the x-y coordinate grid, are points A(m, n) and B(r, t) equidistant

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