The vertices of triangle ABC are A(-5, 2), B(-2, 5), and C(3, 4). Write an equation in slope-intercept form for the line containing the median of triangle ABC through point B.
Can someone please help me figure out how to solve this equation?
Sure
one point on your line is point B (-2 , 5)
the other is the midpoint of AC
average x = (-5+3)/2 = -1
average y = (2+4)/2 = 3
so second point is (-1 , 3)
now I bet you know how to find the equation of the line through
(-2 , 5) and (-1 , 3)
The median is located in the middle of A to C.
Use your midpoint formula to locate it (remember the midpoint is adding up the ((x1 + x2)/2, (y1 + y2)/2)
So the x co-ordinate of the median is (-5 +3)/2
That is -2/2,
which is 1
(1, y)
You find y.
Then use the B coordinate and your median point (that is 2 points and you find the equation of that line : )
Ms Pi typo, means -2/2 is -1
To write an equation in slope-intercept form for the line containing the median of triangle ABC through point B, we need to find the coordinates of the midpoint of the median. The midpoint is the average of the coordinates of the vertices A and C.
Step 1: Find the coordinates of the midpoint
- Coordinates of A: A(-5, 2)
- Coordinates of C: C(3, 4)
To find the midpoint, we average the x-coordinates and the y-coordinates separately.
Average of x-coordinates: (-5 + 3) / 2 = -1
Average of y-coordinates: (2 + 4) / 2 = 3
So, the midpoint M of the median is M(-1, 3).
Step 2: Find the slope of the line passing through the points B and M.
We can use the slope formula: slope = (y2 - y1) / (x2 - x1)
- Coordinates of B: (-2, 5)
- Coordinates of M: (-1, 3)
Slope = (3 - 5) / (-1 - (-2)) = -2 / 1 = -2
Step 3: Use the slope-intercept form equation, y = mx + b, with the slope from step 2 and the coordinates of point B to find the y-intercept b.
Using the coordinates of B (-2, 5) and the slope -2:
5 = -2(-2) + b
5 = 4 + b
b = 5 - 4
b = 1
So, the y-intercept is 1.
Step 4: Write the equation in slope-intercept form, y = mx + b, using the slope from step 2 and the y-intercept from step 3.
Thus, the equation in slope-intercept form for the line containing the median of triangle ABC through point B is:
y = -2x + 1