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LekaFEV [45]
3 years ago
9

Given (9,4) and (x,−11), find all x such that the distance between these two points is 17. Separate multiple answers with a comm

a.
Mathematics
1 answer:
MrRa [10]3 years ago
7 0

Answer:

The points are (1, -11) and (17, -11).

Step-by-step explanation:

The distance between points (x1, y1) and (x2, y2) is

d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

We have values for x1, y1, and y2. We leave x for x2, and we solve for x.

17 = \sqrt{(x - 9)^2 + (-11 - 4)^2}

Square both sides.

289 = (x - 9)^2 + (-11 - 4)^2

289 = x^2 - 18x + 81 + 225

x^2 - 18x + 17 = 0

(x - 1)(x - 17) = 0 [/tex}[tex] x - 1 = 0   or   x - 17 = 0

x = 1 or x = 17

The points are (1, -11) and (17, -11).

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See attached document for better illustration.

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