Find all of the points of the form (x, −1) which are 4 units from the point (3,2)
To find all the points of the form (x, -1) that are 4 units away from the point (3,2), we can use the distance formula.
The distance formula is:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, the coordinates of the point (3,2) are (x1, y1) = (3,2). And we want to find the values of x (x2) for which the distance between the points is 4 units.
Plugging the values into the formula, we get:
4 = √((x2 - 3)^2 + (-1 - 2)^2)
Simplifying the equation, we have:
16 = (x2 - 3)^2 + 9
Expanding and rearranging, we have:
16 - 9 = (x2 - 3)^2
7 = (x2 - 3)^2
Taking the square root of both sides, we get:
√7 = x2 - 3
Now, we can solve for x2 by adding 3 to both sides of the equation:
x2 = 3 + √7
Therefore, the points of the form (x, -1) that are 4 units from the point (3,2) are:
(x, -1) = (3 + √7, -1) and (3 - √7, -1)
To find all the points of the form (x, −1) which are 4 units from the point (3,2), we can use the distance formula. The distance between two points (x1, y1) and (x2, y2) can be calculated using the formula:
Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
In this case, we are given that the point we want to find is 4 units away from (3,2) and its y-coordinate is -1. Let's substitute these values into the distance formula and solve for x.
Distance = 4
x1 = 3
y1 = 2
x2 = x (unknown)
y2 = -1
Using the distance formula, we have:
4 = √[(x - 3)^2 + (-1 - 2)^2]
Simplifying, we get:
16 = (x - 3)^2 + 9
Expanding and rearranging, we have:
0 = (x - 3)^2 - 7
Now, let's solve for x.
(x - 3)^2 = 7
Taking the square root of both sides, we get:
x - 3 = ±√7
Adding 3 to both sides, we have:
x = 3 ± √7
So, the points of the form (x, -1) which are 4 units from the point (3,2) are (3 + √7, -1) and (3 - √7, -1).
(x-3)^2 + (-2-1)^2 = 16
x^2 -6 x + 9 + 9 = 16
x^2 - 6 x + 2 = 0
x = [ 6 +/- sqrt(36 -8) ]/2
x= 3 +/- sqrt 7 and y = -1 of course