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

Question

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

in progress 0
Thiên Ân 18 hours 2021-07-21T23:40:36+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-07-21T23:41:43+00:00

    YZ would be negative 4 to a 2

    0
    2021-07-21T23:42:33+00:00

    9514 1404 393

    Answer:

      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.

    __

    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.

    __

    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.

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )