To find the distance between two points, you can use the distance formula:
Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
Using the point (-4, -3) as (x1, y1), the distance from each of the other points can be calculated as follows:
1. (-4, 16):
Distance = √[(-4 - (-4))^2 + (16 - (-3))^2] = √[(0)^2 + (19)^2] = √(0 + 361) = √361 = 19
2. (5, -3):
Distance = √[(5 - (-4))^2 + (-3 - (-3))^2] = √[(9)^2 + (0)^2] = √(81 + 0) = √81 = 9
3. (-13, -3):
Distance = √[(-13 - (-4))^2 + (-3 - (-3))^2] = √[(-9)^2 + (0)^2] = √(81 + 0) = √81 = 9
4. (-4, -13):
Distance = √[(-4 - (-4))^2 + (-13 - (-3))^2] = √[(0)^2 + (-10)^2] = √(0 + 100) = √100 = 10
5. (-4, 6):
Distance = √[(-4 - (-4))^2 + (6 - (-3))^2] = √[(0)^2 + (9)^2] = √(0 + 81) = √81 = 9
Therefore, the points that have a distance of 9 from the point (-4, -3) are:
- Point (5, -3)
- Point (-13, -3)
- Point (-4, 6)
Which THREE of the following points have a distance of 9 from the point (- 4,- 3)?
*
1 point
(-4, 16)
(5, -3)
(-13, -3)
(-4, -13)
(-4, 6)
7 answers
Two points are plotted in the coordinate plane at (-2, 9) and (-2, -2). What is the distance between them?
To find the distance between two points, you can use the distance formula:
Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
Let's use the points (-2, 9) and (-2, -2) as (x1, y1) and (x2, y2) respectively:
Distance = √[(-2 - (-2))^2 + (-2 - 9)^2]
Distance = √[(0)^2 + (-11)^2]
Distance = √(0 + 121)
Distance = √121
Distance = 11
Therefore, the distance between the points (-2, 9) and (-2, -2) is 11 units.
Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
Let's use the points (-2, 9) and (-2, -2) as (x1, y1) and (x2, y2) respectively:
Distance = √[(-2 - (-2))^2 + (-2 - 9)^2]
Distance = √[(0)^2 + (-11)^2]
Distance = √(0 + 121)
Distance = √121
Distance = 11
Therefore, the distance between the points (-2, 9) and (-2, -2) is 11 units.
Which coordinate pair should be plotted when x = 3 to keep the ratio the same?
To keep the ratio the same when x = 3, we need to find the corresponding y value that maintains the same ratio between the points.
The original coordinate pair is (-2, 9). Let's find the ratio between x and y: x / y = -2 / 9
To keep the ratio the same when x = 3, we can solve for y:
3 / y = -2 / 9
3 * 9 = -2 * y
27 = -2y
y = -27 / 2
y = -13.5
Therefore, the corresponding coordinate pair when x = 3 to keep the ratio the same is (3, -13.5).
The original coordinate pair is (-2, 9). Let's find the ratio between x and y: x / y = -2 / 9
To keep the ratio the same when x = 3, we can solve for y:
3 / y = -2 / 9
3 * 9 = -2 * y
27 = -2y
y = -27 / 2
y = -13.5
Therefore, the corresponding coordinate pair when x = 3 to keep the ratio the same is (3, -13.5).
What are the coordinates for the reflection across the x-axis for point M?
* Point M is -2, 4
* Point M is -2, 4
To find the reflection of a point across the x-axis, you simply change the sign of the y-coordinate of the point.
Given the coordinates of Point M as (-2, 4), the reflection across the x-axis will have the same x-coordinate (-2) but the y-coordinate will have the opposite sign:
The reflection across the x-axis for Point M will be (-2, -4).
Given the coordinates of Point M as (-2, 4), the reflection across the x-axis will have the same x-coordinate (-2) but the y-coordinate will have the opposite sign:
The reflection across the x-axis for Point M will be (-2, -4).