what is the answer of this?the line segment connecting (x,6)and (9,y) is bisected by the point (7,3) find the values of x and y
so (7,3) is the midpoint
remember how to find the midpoint between
(a,b) and (c,d)
midpoint = ( (a+c)/2 , (b+d)/2 )
so if the endpoints are (x,6) and (9,y)
then ( (x+9)/2 , (6+y)/2 ) = (7,3)
(x+9)/2 = 7
x+9 = 14
x = 5
and
(6+y)/2 = 3
6+y = 6
y = 0
x = 5 , y = 0
check:
what is the midpoint of
(5,6) and (9,0) ?
11/2 and 9/2
To find the values of x and y, we can use the midpoint formula. The midpoint of a line segment is the average of the x-coordinates and the average of the y-coordinates of its endpoints.
Let's start with the average of the x-coordinates:
(x + 9) / 2 = 7
Simplifying the equation:
x + 9 = 14
x = 14 - 9
x = 5
Now let's determine the average of the y-coordinates:
(6 + y) / 2 = 3
Simplifying the equation:
6 + y = 6
y = 6 - 6
y = 0
Therefore, the values of x and y are 5 and 0 respectively.
To find the values of x and y, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint M between two points A(x₁, y₁) and B(x₂, y₂) are given by:
M = ((x₁ + x₂)/2, (y₁ + y₂)/2)
In this case, we are given that the line segment connecting (x, 6) and (9, y) is bisected by the point (7, 3). Therefore, the midpoint of the line segment is (7, 3).
Using the midpoint formula, we can set up the following equations:
(7, 3) = ((x + 9)/2, (6 + y)/2)
Simplifying the equation:
7 = (x + 9)/2
3 = (6 + y)/2
To solve for x, we can multiply both sides of the first equation by 2:
14 = x + 9
Subtracting 9 from both sides:
5 = x
To solve for y, we can multiply both sides of the second equation by 2:
6 = 6 + y
Subtracting 6 from both sides:
0 = y
Therefore, the values of x and y are 5 and 0, respectively.