reto wrote:

Attachment:

T6198.png

In the figure above, what is the distance from point P to point Q?

A. √2

B. 1.52−1

C. √(1.52−1)

D. (√2)/2

E. 0.5

The distance between the points is the hypotenuse of a 45-45-90 right triangle. The x- and y-coordinates both have a difference of 0.5.

Or: make a right triangle, with right leg going straight down from point (1.5, 1.5), and base (other leg) going straight across from (1,1). The lines will meet at (1.5, 1).

It's an isosceles right triangle. Each side is (1.5 - 1) = \(\frac{1}{2}\).

As a 45-45-90 triangle, it has sides in ratio \(x: x:

x\sqrt{2}\).

The hypotenuse, the distance between the two points, therefore is \((\frac{1}{2}) *(\sqrt{2})\), or \(\frac{\sqrt{2}}{2}\)

Answer D

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