Question

Find all points on the y-axis which are 7 units from
(−4, 4).

Answer 1

(0, 4 +
`√(33)`) or approx. (0, 9.745)

AND

(0, 4 -
`√(33)`) or approx. (0, -1.745)

Explanation:

Since you are attempting to look for all points on the y-axis that are 7 units away from (-4, 4), you can immediately assume that the x value of the coordinate must be 0.

Following this logic, we know that these points would be 4 units to the right, and x units up and down, to make a total distance of 7. To figure out x, you can use the pythagorean theorem:
`a^2 + b^2 = c^2`.

This gives us the equation:

`4^2 + b^2 = 7^2`

`b^2 = 49-16`

`b^2 = 33`

`b = √(33)`

Now, we know there are 2 points on the y-axis that are a distance 7 away from the point (-4, 4). These points would be (0, 4 ±
`√(33)`)

Therefore, all points on the y-axis 7 units from (-4, 4) would be:

1) (0, 4 +
`√(33)`) or approx. (0, 9.745)

2) (0, 4 -
`√(33)`) or approx. (0, -1.745)

An image is provided (where the red circle represents all points 7 away from (-4, 4), and the blue dots are the 2 points that we solved for above)