In the rectangular coordinate plane points X and Z lie on the same line through the origin and points W and Y lie on the same line through the origin. If a2 + b2 = c2 + d2 and e2 + f2 = g2 + h2, what is the value of length XZ andndash; length WY?a)-2b)-1c)0d)1e)2Correct answer is option 'C'. Can you explain this answer?

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In the rectangular coordinate plane points X and Z lie on the same line through the origin and points W and Y lie on the same line through the origin. If a2 + b2 = c2 + d2 and e2 + f2 = g2 + h2, what is the value of length XZ – length WY?

a)
-2
b)
-1
c)
0
d)
1
e)
2

Correct answer is option 'C'. Can you explain this answer?

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In the rectangular coordinate plane points X and Z lie on the same lin...

To find the distance from the origin to any point in the coordinate plane, we take the square root of the sum of the squares of the point's x- and y-coordinates. So, for example, the distance from the origin to point W is the square root of (a2 + b2). This is because the distance from the origin to any point can be thought of as the hypotenuse of a right triangle with legs whose lengths have the same values as the x- and y-coordinates of the point itself:

We can use the Pythagorean Theorem to determine that a² + b² = p², where p is the length of the hypotenuse from the origin to point W.
We are also told in the question that a² + b² = c² + d², therefore point X and point W are equidistant from the origin. And since e² + f² = g² + h², we know that point Y and point Z are also equidistant from the origin.
If the distance from the origin is the same for points W and X, and for points Z and Y, then the length of WY must be the same as the length of XZ. Therefore, the value of length XZ – length WY must be 0.
The correct answer is C.

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