Question

Find all points with a y-coordinate of 3 whose distance from the point (4, -2) is 6.

a) (0, 3), (8, 3)
b) (1, 3), (7, 3)
c) (2, 3), (6, 3)
d) (-3, 3), (11, 3)

Answer 1

To find the points with a y-coordinate of 3 whose distance from the point (4, -2) is 6, we can use the distance formula. This involves solving a quadratic equation to find the x-coordinates of the points and then substituting them back into the equation of the line to find the corresponding y-coordinates.

Step-by-step explanation:

To find all the points with a y-coordinate of 3 whose distance from the point (4, -2) is 6, we can use the distance formula.

The distance formula is given by:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

In this case, we have:

6 = sqrt((x - 4)^2 + (3 - (-2))^2)

6 = sqrt((x - 4)^2 + 25)

Squaring both sides, we get:

36 = (x - 4)^2 + 25

Expanding the equation, we get:

36 = x^2 - 8x + 16 + 25

Combining like terms, we have:

0 = x^2 - 8x + 5

Now, we can solve this quadratic equation using factoring or the quadratic formula to find the x-coordinates of the points. Once we have the x-coordinates, we can substitute them back into the equation of the line to find the corresponding y-coordinates.