the vertices of ABC are A(1,1) B(7,3) and C(2,6) write and equation of the line that contains the median from c to ab
That line must pass through c (2,6) and the midpoint of ab, which is (4,2)
The slope is (6-2)/(2-4) = -2
y = -2 x + b. Now solve for b, by requiring that
6 = (-2)(2) + b
b = 10 Therefore
y = -2x + 10
To find the equation of the line that contains the median from C to AB, we need to first find the midpoint of AB and then determine the slope of the line passing through C and the midpoint.
Step 1: Find the midpoint of AB
The midpoint formula is given by:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
Let's find the coordinates of the midpoint of AB:
x1 = 1, y1 = 1 (Coordinates of A)
x2 = 7, y2 = 3 (Coordinates of B)
Midpoint = ((1 + 7)/2, (1 + 3)/2)
= (8/2, 4/2)
= (4, 2)
So, the midpoint of AB is M(4, 2).
Step 2: Determine the slope of the line passing through C and the midpoint
The formula for slope (m) is given by:
m = (y2 - y1)/(x2 - x1)
Let's find the slope of the line passing through C and M:
x1 = 2, y1 = 6 (Coordinates of C)
x2 = 4, y2 = 2 (Coordinates of M)
m = (2 - 6)/(4 - 2)
= (-4)/(2)
= -2
So, the slope of the line passing through C and the midpoint is -2.
Step 3: Write the equation of the line
We now have the slope (-2) and the coordinates of a point on the line (C: (2, 6)). We can use the point-slope form of the equation to find the equation of the line.
The point-slope form of an equation is:
y - y1 = m(x - x1)
Plugging in the values:
y - 6 = -2(x - 2)
Expanding the equation:
y - 6 = -2x + 4
Rearranging the equation:
y = -2x + 10
So, the equation of the line that contains the median from C to AB is y = -2x + 10.
To find the equation of the line that contains the median from vertex C to side AB, we need to first determine the coordinates of the midpoint of side AB.
Step 1: Find the midpoint of AB
To find the midpoint of segment AB, we need to average the x-coordinates and the y-coordinates separately.
Let's calculate the x-coordinate of the midpoint of AB:
x-coordinate of midpoint = (x-coordinate of A + x-coordinate of B) / 2
= (1 + 7) / 2
= 8 / 2
= 4
Now let's calculate the y-coordinate of the midpoint of AB:
y-coordinate of midpoint = (y-coordinate of A + y-coordinate of B) / 2
= (1 + 3) / 2
= 4 / 2
= 2
Therefore, the midpoint of segment AB is M(4, 2).
Step 2: Find the slope of the median
The median is a line that connects vertex C with the midpoint of side AB. To find the slope, we need to calculate the difference in y-coordinates divided by the difference in x-coordinates.
Let's calculate the slope of the median:
slope = (y-coordinate of C - y-coordinate of M) / (x-coordinate of C - x-coordinate of M)
= (6 - 2) / (2 - 4)
= 4 / (-2)
= -2
Step 3: Write the equation of the line
Now that we have the slope, we can use it along with one of the points (either C or M) to write the equation of the line using the point-slope form.
Using point M(4, 2), we have:
y - y1 = m(x - x1)
y - 2 = -2(x - 4) (Substituting m = -2 and (x1, y1) = (4, 2))
Expanding the equation:
y - 2 = -2x + 8
y = -2x + 10
Therefore, the equation of the line that contains the median from vertex C to side AB is y = -2x + 10.