The distance between two points in a coordinate plane can be found using the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case, the x-coordinates of the two points are the same (-13), and the y-coordinates are 12 and -77 respectively.
d = sqrt((-13 - (-13))^2 + (12 - (-77))^2)
d = sqrt(0^2 + 89^2)
d = sqrt(0 + 7921)
d = sqrt(7921)
d = 89
Therefore, the distance from (-13, 12) to (-13, -77) is 89 units.
What is the distance from (−13, 12) to (−13, −77) ?
11 answers
What is the distance from (−13, 12) to (−13, −77) ?
The distance between two points on the same vertical line is simply the absolute difference between the y-coordinates.
In this case, the y-coordinate of the first point is 12 and the y-coordinate of the second point is -77.
So, the distance is |12 - (-77)| = |12 + 77| = 89 units.
Therefore, the distance from (-13, 12) to (-13, -77) is 89 units.
In this case, the y-coordinate of the first point is 12 and the y-coordinate of the second point is -77.
So, the distance is |12 - (-77)| = |12 + 77| = 89 units.
Therefore, the distance from (-13, 12) to (-13, -77) is 89 units.
Question
Which of the following points has a distance of 10 from the point (−1, 2) ?(1 point)
Which of the following points has a distance of 10 from the point (−1, 2) ?(1 point)
To find points that are at a distance of 10 from the point (-1, 2), we need to consider points that satisfy the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2) = 10
Let's find the points that satisfy this equation.
The points that have a distance of 10 from (-1, 2) are:
1. (-1, 12)
2. (-9, 2)
3. (9, 2)
4. (-1, -8)
Therefore, the points that have a distance of 10 from (-1, 2) are (-1, 12), (-9, 2), (9, 2), and (-1, -8).
d = sqrt((x2 - x1)^2 + (y2 - y1)^2) = 10
Let's find the points that satisfy this equation.
The points that have a distance of 10 from (-1, 2) are:
1. (-1, 12)
2. (-9, 2)
3. (9, 2)
4. (-1, -8)
Therefore, the points that have a distance of 10 from (-1, 2) are (-1, 12), (-9, 2), (9, 2), and (-1, -8).
are u sure
Apologies for the incorrect response. Let's correct it.
To find points that are at a distance of 10 from the point (-1, 2), we can use the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2) = 10
Substituting the coordinates of the given point (-1, 2), we have:
10 = sqrt((x - (-1))^2 + (y - 2)^2)
Simplifying the equation and squaring both sides, we get:
100 = (x - (-1))^2 + (y - 2)^2
Expanding and rearranging, we have:
100 = (x + 1)^2 + (y - 2)^2
Now, let's substitute different values for x and solve for y to find the points that satisfy this equation.
If x = 0, we have:
100 = (0 + 1)^2 + (y - 2)^2
100 = 1 + (y - 2)^2
(y - 2)^2 = 99
y - 2 = ±√99
y = 2 ± √99
So, one of the points that has a distance of 10 from (-1, 2) is (0, 2 + √99).
For x = -2, we have:
100 = (-2 + 1)^2 + (y - 2)^2
100 = 1 + (y - 2)^2
(y - 2)^2 = 99
y - 2 = ±√99
y = 2 ± √99
So, another point that has a distance of 10 from (-1, 2) is (-2, 2 + √99).
In summary, the points that have a distance of 10 from (-1, 2) are (0, 2 + √99) and (-2, 2 + √99).
To find points that are at a distance of 10 from the point (-1, 2), we can use the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2) = 10
Substituting the coordinates of the given point (-1, 2), we have:
10 = sqrt((x - (-1))^2 + (y - 2)^2)
Simplifying the equation and squaring both sides, we get:
100 = (x - (-1))^2 + (y - 2)^2
Expanding and rearranging, we have:
100 = (x + 1)^2 + (y - 2)^2
Now, let's substitute different values for x and solve for y to find the points that satisfy this equation.
If x = 0, we have:
100 = (0 + 1)^2 + (y - 2)^2
100 = 1 + (y - 2)^2
(y - 2)^2 = 99
y - 2 = ±√99
y = 2 ± √99
So, one of the points that has a distance of 10 from (-1, 2) is (0, 2 + √99).
For x = -2, we have:
100 = (-2 + 1)^2 + (y - 2)^2
100 = 1 + (y - 2)^2
(y - 2)^2 = 99
y - 2 = ±√99
y = 2 ± √99
So, another point that has a distance of 10 from (-1, 2) is (-2, 2 + √99).
In summary, the points that have a distance of 10 from (-1, 2) are (0, 2 + √99) and (-2, 2 + √99).
is the answer (-11, 2)
Apologies for the confusion. Let's check if (-11, 2) is a point that has a distance of 10 from (-1, 2).
Using the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Substituting the coordinates of the two points:
d = sqrt((-11 - (-1))^2 + (2 - 2)^2)
d = sqrt((-11 + 1)^2 + (0)^2)
d = sqrt((-10)^2 + 0^2)
d = sqrt(100 + 0)
d = sqrt(100)
d = 10
Since the distance between (-11, 2) and (-1, 2) is indeed 10 units, the point (-11, 2) is correct. Thank you for pointing that out!
Using the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Substituting the coordinates of the two points:
d = sqrt((-11 - (-1))^2 + (2 - 2)^2)
d = sqrt((-11 + 1)^2 + (0)^2)
d = sqrt((-10)^2 + 0^2)
d = sqrt(100 + 0)
d = sqrt(100)
d = 10
Since the distance between (-11, 2) and (-1, 2) is indeed 10 units, the point (-11, 2) is correct. Thank you for pointing that out!
u sure
Apologies for the incorrect response. Let's check if (-11, 2) is a point that has a distance of 10 from (-1, 2).
Using the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Substituting the coordinates of the two points:
d = sqrt((-11 - (-1))^2 + (2 - 2)^2)
d = sqrt((-11 + 1)^2 + (0)^2)
d = sqrt((-10)^2 + 0^2)
d = sqrt(100 + 0)
d = sqrt(100)
d = 10
Since the distance between (-11, 2) and (-1, 2) is indeed 10 units, the point (-11, 2) is correct.
Using the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Substituting the coordinates of the two points:
d = sqrt((-11 - (-1))^2 + (2 - 2)^2)
d = sqrt((-11 + 1)^2 + (0)^2)
d = sqrt((-10)^2 + 0^2)
d = sqrt(100 + 0)
d = sqrt(100)
d = 10
Since the distance between (-11, 2) and (-1, 2) is indeed 10 units, the point (-11, 2) is correct.
0 answers