Find the value of k if p(4,-2) is the midpoint of the line segment joining the point A. (5k,3)and B(-k,-7)
To find the value of k if p(4, -2) is the midpoint of the line segment joining A (5k, 3) and B (-k, -7), we need to use the midpoint formula.
The midpoint formula states that the coordinates of the midpoint are the average of the corresponding coordinates of the endpoints.
Using this formula, we can write the following equations:
Midpoint formula for x-coordinates:
(5k + (-k))/2 = 4
Simplifying the equation:
4k/2 = 4
2k = 4
k = 2
Midpoint formula for y-coordinates:
(3 + (-7))/2 = -2
Simplifying the equation:
(-4)/2 = -2
Therefore, the value of k is 2.
To find the value of k, we need to use the midpoint formula. The midpoint formula states that the coordinates of the midpoint, (x,y), between two points, (x₁, y₁) and (x₂, y₂), is given by:
x = (x₁ + x₂) / 2
y = (y₁ + y₂) / 2
In this case, we are given the midpoint p(4, -2) and the coordinates of points A (5k, 3) and B (-k, -7).
Let's use the formula using the given values:
For the x-coordinate:
4 = (5k + (-k)) / 2
Multiplying both sides by 2: 8 = 5k - k
Combining like terms: 8 = 4k
Dividing both sides by 4: k = 2
So, the value of k that makes p(4, -2) the midpoint of the line segment joining points A and B is k = 2.
Well, to find the value of k, we need to determine the coordinates of the midpoint first.
The midpoint formula is given by:
M = ((x1 + x2)/2 , (y1 + y2)/2)
Using this formula, we can calculate the midpoint of the line segment joining A and B.
Let's plug in the given values:
M = ((5k + (-k))/2 , (3 + (-7))/2)
Simplifying this equation further, we get:
M = ((4k)/2, (-4)/2)
M = (2k, -2)
Now, we know that the midpoint is (4, -2).
Since M = (2k, -2), we can equate the x-coordinate and y-coordinate:
2k = 4
Solving for k, we find:
k = 2
So, the value of k is 2.
Therefore, the value of k for p(4,-2) to be the midpoint is 2.
Let the point p[4,-2] =[x1,y1]
a[....] =[x2,y2]
B[....] =[x3,y3]
Now put the value in this formula,
1/2[x1(y2-y3)+x2(y3-y1)+x3(y1-y2)]=O
Your answer will be 2. I mean value of k will be 2
Recall your method of finding the midpoint:
For the x of the midpoint, add the x values of the endpoints, then divide by 2 (in effect you are taking the average of the x's)
For the y of the midpoint .... (same thing)
let's check if they did the y value correctly.
( 3 + (-7))/2
= -4/2
= -2
yup, that's what they have as the midpoint y value
now repeat for the x value, and find k
let me know what you got.