given points : p (2,1) q (-4,2) m(5,3) find the coordinates of a point n such that pq and mn are parallel find coordinate of a point k such that mk is perpendicular to pq
slope from p to q = (2-1)/(-4-2) = -1/6
so find n so that mn has slope of -1/6
pick any old n for n, for example x = 0
then
-1/6 = (Yn -3)/(0 - 5) = (Yn - 3) /-5
5/6 = Yn - 3
Yn = 3 5/6 = 23/6
so n (0, 23/6)
now do the same for slope = -1/(-1/6) = 6
hey damon i need help on mine
thank u
so how do i find the slope?
the slope of the perpendicular = -1/slope of original
m' = -1 / (-1/6) = 6
Oh, slope = (Y2-Y1)/(X2-X1)
To find the coordinates of point N, we need to find a point that is parallel to line PQ, which passes through point M.
1. Find the slope of line PQ:
The slope of a line passing through two points (x1, y1) and (x2, y2) can be calculated using the formula:
slope = (y2 - y1) / (x2 - x1)
Let's calculate the slope of line PQ:
slope_PQ = (2 - 1) / (-4 - 2) = 1 / (-6) = -1/6
2. Apply the slope value to point M:
We can use the slope-intercept form of a line equation:
y = mx + b
where m represents the slope of the line. Since PQ and MN are parallel, they have the same slope.
Let's calculate the equation using point M:
3 = (-1/6) * 5 + b
3 = -5/6 + b
b = 3 + 5/6 = 18/6 + 5/6 = 23/6
So the equation of the line passing through point M is:
y = (-1/6)x + 23/6
3. Find point N:
To find the coordinates of point N, we need to substitute the x-coordinate of point M into the equation:
y = (-1/6) * 2 + 23/6
y = -2/6 + 23/6
y = 21/6 = 7/2
So the coordinates of point N are (2, 7/2).
To find the coordinates of point K, which is perpendicular to line PQ passing through point M, we need to determine the slope of line MK and then find its negative reciprocal.
4. Calculate the slope of line MK:
The slope of line MK can be found using the formula we used earlier using points M and K.
Let's calculate the slope of line MK:
slope_MK = (y_K - y_M) / (x_K - x_M)
Since we don't have the coordinates of point K, we'll use the negative reciprocal of the slope of line PQ.
slope_MK = -1 / slope_PQ
slope_MK = -1 / (-1/6)
slope_MK = 6
5. Apply the slope value to point M:
Using point M and the slope value, we can derive the equation of line MK.
Let's calculate the equation using point M:
3 = 6 * 5 + b
3 = 30 + b
b = 3 - 30 = -27
So the equation of the line passing through point M is:
y = 6x - 27
6. Find point K:
To find the coordinates of point K, we need to substitute the y-coordinate of point M into the equation:
3 = 6x - 27
30 = 6x
x = 5
So the coordinates of point K are (5, 3).
Therefore, the coordinates of point N are (2, 7/2) and the coordinates of point K are (5, 3).