find y so that the distance between the points is 8:

(0,0) (3,y)

using the distance formula..

8=sqrt (3^2 + y^2)
square bot sides.
64=9+y^2
subtract 9 from both sides
55=y^2
y=sqrt 55

The distance formula is just the pythagorean theorem(x^2+y^2=hypotenuse^2). If you know x (0+3=3) and you know the hypotenuse (8), you can find y.

3^2 + y^2 = 8^2
9 + y^2 = 64
y^2 = 55
y = sqrt(55)

To find the value of y such that the distance between the points (0,0) and (3,y) is 8, you can use the distance formula.

The distance formula is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

In this case, (x1, y1) = (0,0) and (x2, y2) = (3,y). We want to find y when the distance d is equal to 8:

8 = sqrt((3 - 0)^2 + (y - 0)^2)

Simplifying the equation, we have:

64 = (3^2) + y^2

64 = 9 + y^2

Subtracting 9 from both sides, we get:

55 = y^2

Taking the square root of both sides, we have:

√55 = y

So, the value of y that satisfies the condition is y = √55 (approximately 7.42).

Therefore, when y is approximately 7.42, the distance between the points (0,0) and (3,y) will be 8.