find all points having an x-coordinate of 2 whose distance of the point (-1-2)is 5.
all points having a distance of 5 from (-1, -2) lie on a circle with equation
(x+1)^2 + (y+2)^2 = 25
you want the x to be 2
3^2 + (y+2)^2 = 25
(y+2)^2 = 16
y + 2 = ± √ 16 = ± 4
if y+2 = 4, then y = 2
if y+2 = -4, then y = -6
so your points are (2,2) and (2,-6)
Oh, finding points can feel like a game of hide and seek! Let's go on an adventure to seek those points, shall we?
To find all points having an x-coordinate of 2, we need to look for spots on the x-axis where x = 2. Got it? Good!
Now, let's move on to the distance part. We're given that the point (-1, -2) is 5 units away. So, we're essentially looking for points that are 5 units away from (-1, -2).
Now, let's put on our mathematical hats and solve this riddle!
There are two points that satisfy this condition. The first point is (2, 3) because it has an x-coordinate of 2 and is 5 units away from (-1, -2) when measured using the shortest path possible. You can visualize this by connecting (-1, -2) and (2, 3) with a straight line.
The second point is (2, -7) because it also has an x-coordinate of 2 and is 5 units away from (-1, -2) when measured using the shortest path possible. Just like the first point, you can connect (-1, -2) and (2, -7) with a straight line to visualize it.
So, there you have it! The two points with an x-coordinate of 2 and a distance of 5 from (-1, -2) are (2, 3) and (2, -7). Happy exploring, my friend!
To find all the points that have an x-coordinate of 2 and a distance of 5 units from the point (-1, -2), we can use the distance formula. The distance formula is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Using this formula, we can substitute the given values:
5 = sqrt((2 - (-1))^2 + (y - (-2))^2)
Simplifying this equation, we have:
25 = (2 + 1)^2 + (y + 2)^2
25 = 3^2 + (y + 2)^2
25 = 9 + (y + 2)^2
Subtracting 9 from both sides, we get:
16 = (y + 2)^2
Now, we can take the square root of both sides:
±4 = y + 2
Solving for y, we have:
y = -2 ± 4
Therefore, the two possible points with an x-coordinate of 2 and a distance of 5 units from the point (-1, -2) are:
(2, -6) and (2, 2)
To find all the points with an x-coordinate of 2 that are a distance of 5 units away from the point (-1, -2), we can use the distance formula. The distance formula between two points (x1, y1) and (x2, y2) is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Let's substitute the given values into the distance formula:
5 = √((2 - (-1))^2 + (y - (-2))^2)
Simplifying the equation, we have:
25 = (2 - (-1))^2 + (y + 2)^2
25 = (2 + 1)^2 + (y + 2)^2
25 = 3^2 + (y + 2)^2
25 = 9 + (y + 2)^2
Solving for (y + 2)^2, we have:
(y + 2)^2 = 25 - 9
(y + 2)^2 = 16
Taking the square root of both sides, we get:
y + 2 = ±√16
y + 2 = ±4
Solving for y in both cases, we have:
Case 1: y + 2 = 4
y = 4 - 2
y = 2
Case 2: y + 2 = -4
y = -4 - 2
y = -6
Therefore, the points with an x-coordinate of 2 that are a distance of 5 units away from the point (-1, -2) are:
(2, 2) and (2, -6).