Enter your answer and show all the steps that you use to solve this problem in the space provided. The midpoint of CD¯¯¯¯¯ is E(−1,0) . One endpoint is C(5,2) . What are the coordinates of the other endpoint?
Enter your answer and show all the steps that you use to solve this problem in the space provided. PB¯¯¯¯¯ is a line segment on a number line. It has endpoints at −2 and 12. What is the coordinate of its midpoint? (2 points)
Enter your answer and show all the steps that you use to solve this problem in the space provided. Explain the distance formula. Then use it to calculate the distance between A(1, 1) and B(7,−7)
please help
To find the coordinates of the other endpoint, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint between two points (x₁, y₁) and (x₂, y₂) is given by the average of the x-coordinates and the average of the y-coordinates.
Given that the midpoint E is (-1, 0) and one endpoint C is (5, 2), we can let the coordinates of the other endpoint be (x, y).
The x-coordinate of the midpoint is the average of the x-coordinates of C and (x, y):
(-1) = (5 + x)/2
Multiplying both sides by 2, we have:
-2 = 5 + x
Subtracting 5 from both sides, we get:
x = -7
The y-coordinate of the midpoint is the average of the y-coordinates of C and (x, y):
0 = (2 + y)/2
Multiplying both sides by 2, we have:
0 = 2 + y
Subtracting 2 from both sides, we get:
y = -2
Therefore, the coordinates of the other endpoint are (-7, -2).
For the second problem, the coordinate of the midpoint of PB¯¯¯¯¯ can be found by taking the average of the coordinates of the endpoints -2 and 12.
The midpoint is given by:
Midpoint = (Endpoint₁ + Endpoint₂)/2
Midpoint = (-2 + 12)/2
Midpoint = 10/2
Midpoint = 5
Therefore, the coordinate of the midpoint of PB¯¯¯¯¯ is 5.
The distance formula is a formula used to find the distance between two points in a coordinate plane. It is derived from the Pythagorean theorem. The distance between two points (x₁, y₁) and (x₂, y₂) is given by:
Distance = √((x₂ - x₁)² + (y₂ - y₁)²)
Using the distance formula, we can calculate the distance between point A(1, 1) and point B(7, -7):
Distance = √((7 - 1)² + (-7 - 1)²)
Distance = √(6² + (-8)²)
Distance = √(36 + 64)
Distance = √100
Distance = 10
Therefore, the distance between point A(1, 1) and point B(7, -7) is 10.
Sure! I can help you with these problems step by step.
Problem 1:
We are given that the midpoint of CD¯¯¯¯¯ is E(-1,0) and one endpoint is C(5,2). We need to find the coordinates of the other endpoint.
To find the midpoint of a line segment, we use the formula:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
Let the coordinates of the other endpoint be D(x,y).
Using the midpoint formula, we can write the equation:
(-1,0) = ((5 + x) / 2, (2 + y) / 2)
Now let's solve for x and y:
(5 + x) / 2 = -1
Solving for x:
5 + x = -2
x = -2 - 5
x = -7
Substitute the value of x into the equation and solve for y:
(2 + y) / 2 = 0
2 + y = 0
y = 0 - 2
y = -2
Therefore, the coordinates of the other endpoint are D(-7,-2).
Problem 2:
We are given that PB¯¯¯¯¯ is a line segment on a number line with endpoints at -2 and 12. We need to find the coordinate of its midpoint.
To find the midpoint of a line segment on a number line, we use the formula:
Midpoint = (x1 + x2) / 2
Let the coordinates of the midpoint be M(x).
Using the midpoint formula, we can write the equation:
M = (-2 + 12) / 2
Simplifying the equation:
M = 10 / 2
M = 5
Therefore, the coordinate of the midpoint is 5.
Problem 3:
The distance formula calculates the distance between two points, A(x1, y1) and B(x2, y2), in a coordinate plane using the Pythagorean theorem. The formula is:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
To calculate the distance between A(1,1) and B(7,-7), we substitute the values into the distance formula:
Distance = √((7 - 1)^2 + (-7 - 1)^2)
Distance = √(6^2 + (-8)^2)
Distance = √(36 + 64)
Distance = √100
Distance = 10
Therefore, the distance between A(1,1) and B(7,-7) is 10.
To find the coordinates of the other endpoint of CD¯¯¯¯¯, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) are given by the averages of the corresponding coordinates:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
In this case, we know that the midpoint is E(-1, 0), and one endpoint is C(5, 2). Let's substitute these values into the formula:
(-1) = ((5 + x2) / 2)
0 = ((2 + y2) / 2)
Solving the first equation, we can multiply both sides by 2 to clear the fraction:
-2 = 5 + x2
x2 = -7
Solving the second equation similarly, we get:
0 = 2 + y2
y2 = -2
Thus, the coordinates of the other endpoint of CD¯¯¯¯¯ are (-7, -2).
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To find the coordinate of the midpoint of PB¯¯¯¯¯ on a number line, we can use the midpoint formula. The midpoint formula for a line segment with endpoints a and b is:
Midpoint = (a + b) / 2
In this case, the endpoints of PB¯¯¯¯¯ are -2 and 12. Let's substitute these values into the formula:
Midpoint = (-2 + 12) / 2
Midpoint = 10 / 2
Midpoint = 5
Therefore, the coordinate of the midpoint of PB¯¯¯¯¯ is 5.
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The distance formula is a formula used to calculate the distance between two points in a coordinate plane. The formula is derived from the Pythagorean theorem, and it states:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, we have two points A(1, 1) and B(7, -7). Let's substitute these values into the formula:
Distance = √((7 - 1)^2 + (-7 - 1)^2)
Distance = √(6^2 + (-8)^2)
Distance = √(36 + 64)
Distance = √100
Distance = 10
Therefore, the distance between A(1, 1) and B(7, -7) is 10 units.