mgmat b

[resilient]

In the rectangular coordinate system, are the points (a, b) and (c, d) equidistant from the origin?

(1) a/b = c/d

(2) root a^2 + root b^2 = root c^2+ root d^2

is there a way to do this without the distance formula? Can we try to prove this with proving numbers?

I do like taking the average of the numbers in order to get the distance. (mgmat trick) However, I was unsuccesful during the question.

qa is
c

[netigen]

(A) is definitely not sufficient

(B) in itself is also not sufficient

Lets look at A again

a/b = c/d

square both sides

a^2/b^2 = c^2/d^2

now sq rt

sqrt(a^2)/sqrt(b^2) = sqrt(c^2)/sqrt(d^2)

add 1 to both sides

we get

(root a^2 + root b^2)/root b^2 = (root c^2+ root d^2)/root d^2

using B this can be reduced to

|b| = |d|

similarly we can show that |a| = |c|

so both A and B together should be sufficient.

BTW this definitely is not a 2 min question

[leovonp]

Sorry netigen, but I don't get how you reduced to b = d.

Could show it step by step please?

Thx

[netigen]

(root a^2 + root b^2)/root b^2 = (root c^2+ root d^2)/root d^2

We already know from (B)

(root a^2 + root b^2) = (root c^2+ root d^2)

Hence, the eq gets reduced to

1/root b^2 = 1/root d^2

root d^2 = root b^2

or |d| = |b|