I'm confused on how to do this. algebra M(X,Y) is midpoint of CD with endpoints C(5,9) and D(17,29).
Find the values of X and Y.
Show the MC = MD.
Well, solving this algebra problem might make you feel like you're in a bit of a circus, but don't worry, I'm here to clown around and help you out!
To find the values of X and Y for the midpoint M(X,Y), we can use the midpoint formula. According to that, the coordinates of the midpoint are the average of the coordinates of the endpoints. In other words:
X = (X_C + X_D) / 2
Y = (Y_C + Y_D) / 2
Substituting the given values, we have:
X = (5 + 17) / 2
Y = (9 + 29) / 2
Now, let's calculate:
X = 22 / 2
Y = 38 / 2
Simplifying further:
X = 11
Y = 19
So, X = 11 and Y = 19 are the values for the midpoint M(X,Y) of the line segment CD.
Now, let's show that MC = MD.
To do that, we need to calculate the length of MC and MD. The distance formula will come in handy here:
MC = √((X_M - X_C)^2 + (Y_M - Y_C)^2)
MD = √((X_M - X_D)^2 + (Y_M - Y_D)^2)
Substituting the values:
MC = √((11 - 5)^2 + (19 - 9)^2)
MD = √((11 - 17)^2 + (19 - 29)^2)
Let's do the math:
MC = √(6^2 + 10^2)
MD = √((-6)^2 + (-10)^2)
Simplifying further:
MC = √(36 + 100)
MD = √(36 + 100)
MC = √136
MD = √136
So, MC = MD, both equal to √136.
I hope this math circus act wasn't too confusing! If you have any other questions, feel free to ask.
To find the values of X and Y for the midpoint M(X, Y) of CD with endpoints C(5,9) and D(17,29), we need to use the midpoint formula.
The midpoint formula states that the coordinates of the midpoint (X, Y) between two endpoints (x1, y1) and (x2, y2) is given by:
X = (x1 + x2) / 2
Y = (y1 + y2) / 2
Using this formula, we can substitute the values for C(5,9) and D(17,29) to find X and Y.
X = (5 + 17) / 2
= 22 / 2
= 11
Y = (9 + 29) / 2
= 38 / 2
= 19
Therefore, the values of X and Y for the midpoint M(X, Y) are X = 11 and Y = 19.
To show that MC = MD, we can calculate the distances using the distance formula.
The distance formula states that the distance between two points (x1, y1) and (x2, y2) is given by:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Using this formula, we can calculate the distances MC and MD using the coordinates of the points M, C, and D.
MC = sqrt((X - x1)^2 + (Y - y1)^2)
= sqrt((11 - 5)^2 + (19 - 9)^2)
= sqrt(6^2 + 10^2)
= sqrt(36 + 100)
= sqrt(136)
≈ 11.66
MD = sqrt((X - x2)^2 + (Y - y2)^2)
= sqrt((11 - 17)^2 + (19 - 29)^2)
= sqrt((-6)^2 + (-10)^2)
= sqrt(36 + 100)
= sqrt(136)
≈ 11.66
As we can see, MC and MD have the same value of approximately 11.66. This shows that MC = MD, satisfying the condition for midpoint.
To find the values of X and Y, let's start by using the midpoint formula. The midpoint formula states that the midpoint M between two points (x1, y1) and (x2, y2) is given by the coordinates ( (x1 + x2) / 2, (y1 + y2) / 2 ).
In this case, the coordinates of the endpoints are:
C(5, 9)
D(17, 29)
We need to find the midpoint, M(X, Y). The x-coordinate of the midpoint is obtained by taking the average of the x-coordinates of C and D, and the y-coordinate is obtained by taking the average of the y-coordinates of C and D.
So, let's calculate X first:
X = (x1 + x2) / 2 = (5 + 17) / 2 = 22 / 2 = 11
Now, let's calculate Y:
Y = (y1 + y2) / 2 = (9 + 29) / 2 = 38 / 2 = 19
Therefore, the values of X and Y are X = 11 and Y = 19.
To show that MC = MD, we need to calculate the distances MC and MD using the distance formula. The distance formula states that the distance between two points (x1, y1) and (x2, y2) is given by the square root of [(x2 - x1)^2 + (y2 - y1)^2].
The coordinates of M are (11, 19), and the coordinates of C are (5, 9), so let's calculate MC:
MC = sqrt[(x2 - x1)^2 + (y2 - y1)^2] = sqrt[(11 - 5)^2 + (19 - 9)^2] = sqrt[36 + 100] = sqrt[136]
The coordinates of M are (11, 19), and the coordinates of D are (17, 29), so let's calculate MD:
MD = sqrt[(x2 - x1)^2 + (y2 - y1)^2] = sqrt[(17 - 11)^2 + (29 - 19)^2] = sqrt[36 + 100] = sqrt[136]
As you can see, both MC and MD have the same value of sqrt[136], which means they are equal. Therefore, MC = MD.
The x-coordinate of M is halfway between the x-coordinates of C and D. That is the average value: (5+17)/2 = 11
Same for y: (9+29)/2 = 19
So, M = (11,19)
MC = √((11-5)^2 + (19-9)^2) = √(6^2+10^2) = √136
MD = √((17-11)^2+(29-19)^2) = √(6^2+10^2) = √136