In a right triangle, the hypotenuse has endpoints XY, shown on the graph. On a coordinate plane, line X Y has points (negative 4, 2), (negative 1, negative 3).

If Z represents the third vertex in the triangle and is located in the second quadrant with integer coordinates, what is the length of YZ?
3
4
5
6

9514 1404 393

  5

Step-by-step explanation:

A graph can be helpful. It shows possible integer coordinates of Z could be ...

  (-1, 2) or (-5, 1)

These have distances 5 and 4√2 from Y, respectively. Of these, only the length YZ = 5 appears on your list of possible answers.

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The hypotenuse of a right triangle is the diameter of the circumcircle. That is, the right angle vertex (Z) appears on a circle whose center is the midpoint of the hypotenuse. Here, that circle center is C = (-4-1, 2-3)/2 = (-5/2, -1/2). The given point Y differs from this by C - Y = (-5/2 -(-1), -1/2 -(-3)) = (-3/2, 5/2). So, a point with integer coordinates will be 2×(5/2) = 5 units above point Y, which puts it in the 2nd quadrant.

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Adding any of the 8 combinations (±3/2, ±5/2) or (±5/2, ±3/2) to the circle center coordinates will result in integer coordinates for the right angle vertex. Of these, only the ones listed above are in the second quadrant. A couple are on the y-axis, and two of the possibilities are X and Y. The other two are in the third quadrant.

whole numbers.

step-by-step explanation:

we are given the average monthly rainfall (in millimeters) model r(m) for the years 1900-2009 as a function of the month number m.

as we can see m is taken for the number of months for years 1900-2009.

we know that number of months can't be a negative number or decimal number or a fraction.

so, the number of months could be only positive whole numbers.

therefore, whole numbers is more appropriate for the domain of r.

answer: the distance

step-by-step explanation:

to calculate the distance d of a line segment with endpoints (x1, y1) and (x2, y2) use the formula d (x2 x1)2 (y2 y1)2. to calculate the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) use the formula