Question

The distance between two points is √39 One endpoint is (4,−3). It is known that the y-coordinate of the other endpoint is 2.

Answer 1

Answer:

$(4-\sqrt{14}, 2)\text{ or } (4+\sqrt{14}, 2)$

Step-by-step explanation:

We have the two points: (4, -3) and (x, 2).

We know that the distance between them is √39.

To find our x-coordinate of the second point, we can use the distance formula:

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

Let (4, -3) be (x₁, y₁) and let (x, 2) be (x₂, y₂). We also know that the distance d is √39. Substitute:

$\sqrt{39}=\sqrt{(x-4)^2+(2-(-3))^2$

Solve for x. First, let's square both sides. This cancels out the square roots:

$39=(x-4)^2+(2+3)^2$

Evaluate the second term on the right:

$39=(x-4)^2+(5)^2$

Square:

$39=(x-4)^2+25$

Subtract 25 from both sides:

$14=(x-4)^2$

Take the square root of both sides. Since we're taking an even root, we need plus/minus. So:

$x-4=\pm\sqrt{14}$

Add 4 to both sides:

$x=4\pm\sqrt{14}$

Therefore, there exists two possibilities for our second point. It can either be:

$(4-\sqrt{14}, 2)\text{ or } (4+\sqrt{14}, 2)$

And we're done!