Line segment HJ has a length of 17. Find y given H (-4,16) and J (-12,y) then find another possible value for y.

Answer 1

Let’s start with a rough sketch so we know what we’re dealing with. We know H is (-4,16) and the J lies somewhere along the line x=-12, so we can plot it like this:

The horizontal distance from J to H is 8, and the hypotenuse is 17, so this is the 8,15,17 right triangle (you can also use Pythagorean Theorem).

From the graph, we can see that

y = 16-15, so

 y=1 is the answer.

There is another solution:

Point J can also be higher than point H. In this case,

 y=16+15

y = 31 another answer

Point J is at either at (-12, 1) or (-12,31).

Answer 2

(-4,16) to (-12,y) = 17

use the pythagorean theorem, or it's called the distance formula

d^2 = c^2 = a^2 +b^2

17^2 = 64+ (y-16)^2

y^2 -32y + 256 +64 = 289

y^2 -32y - 31 = 0 which almost has integer factors (y-32)(y+1)=0 with y = 32 or -1 which is fairly close

but instead use the quadratic formula

or complete the square

y^2-32y +16^2 = 31 +16^2

(y-16)^2 = 287

y-16 = +/-sqr287

y = 16 +/-16.94

y = 32.94 or -0.94

y= about 33 or -1