Find all points having x-coordinate 9 and distance 10 from the point (3,-2).
Would I use the distance formula here?
Yes, you would use the distance formula to find the points that are 10 units away from the point (3,-2) and have an x-coordinate of 9. The distance formula is given by:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case, the x-coordinate of the point we are looking for is 9, so x2 = 9. The x-coordinate of the given point (3,-2) is x1 = 3. We want the distance to be 10, so Distance = 10. Plugging these values into the formula, we get:
10 = sqrt((9 - 3)^2 + (y2 - (-2))^2)
Simplifying the equation, we have:
100 = (9 - 3)^2 + (y2 + 2)^2
100 = 36 + (y2 + 2)^2
(y2 + 2)^2 = 100 - 36
(y2 + 2)^2 = 64
Now, we can solve for y2 by taking the square root of both sides:
y2 + 2 = ±sqrt(64)
y2 + 2 = ±8
Solving for y2, we have two possible values:
1. y2 + 2 = 8 -> y2 = 8 - 2 = 6
2. y2 + 2 = -8 -> y2 = -8 - 2 = -10
Therefore, the two points that have an x-coordinate of 9 and distance 10 from the point (3,-2) are (9, 6) and (9, -10).