Question

He knows the right triangle JAM contains points J (-3,8) and M (5,4) but the Psl spilled right on his coordinates for A so he only knows that x - coordinate of A is 1. If the triangle is a right triangle, what are the possibilities for the y - coordinate of point A

Answer 1

Four Answers:

10.4721 approximately

1.5279 approximately

-4

16

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Step-by-step explanation:

Use the midpoint formula to find that N = (1,6) is the midpoint of J(-3,8) and M(5,4). I'm skipping steps so let me know if you need to see them.

Then draw a circle centered at N with radius NM. The equation of this circle is (x-1)^2+(y-6)^2 = 20

Plug in x = 1 and solve for y to get y = 10.4721 and y = 1.5279

These values are approximate.

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The equation of line MJ is y = -0.5x + 6.5 where both decimal values are exact.

The slope here is m = -0.5 which has the negative reciprocal of 2, and this is the perpendicular slope.

The line perpendicular to MJ, that goes through M, is y = 2x-6

Plug in x = 1 to find that y = 2(1)-6 = -4

The line perpendicular to MJ, that goes through J, is y = 2x+14

Plug in x = 1 to find that y = 2(1)+14 = 16

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The diagram below shows points in red of all the possible locations point A could be.