The question says determine the coorinates of the pointd M on the x-axis so that AB is perpendicular to MN, given the points A(5,3), B(-2,4) and N (-3,-7)
the slope of AB is 1/-7 so the reciprocal is 7/1 which is what the slope of MN has to equal. but how do i find the coordinates of M.
Perpendicular Line Slope Math Question?
2008-01-05 12:53 am
回答 (7)
2008-01-05 1:01 am
✔ 最佳答案
Equation of linear lines: m= y2-y1/x2-x1
*OR*
y2-y1 = m(x2-x1)
We know N is a point on the line of MN with coordinates (-3,-7)
We know that the slope is 7
We know that the point M has the coordinates (x1,0) <--x-axis
y2-y1 = m(x2-x1)
(-7)-(0) = (7)((-3)-x1)
-7 = 7(-3-x1)
-1 = -3 - x1
x1 = -3 +1
x1 = -2
So point M's coordinates are (-2,0)
2008-01-10 12:51 pm
Slope = 7
Equation of linear line is:
y-y1 = 7(x-x1)
It passes N(-3, -7)
y - (-7) = 7 (x -(-3))
y +7 = 7 (x + 3)
Since the point M is on x- axis, so M's y coordinate is 0
0 + 7 = 7x + 21
-14 = 7x
-2 = x
Answer is (-2, 0)
Equation of linear line is:
y-y1 = 7(x-x1)
It passes N(-3, -7)
y - (-7) = 7 (x -(-3))
y +7 = 7 (x + 3)
Since the point M is on x- axis, so M's y coordinate is 0
0 + 7 = 7x + 21
-14 = 7x
-2 = x
Answer is (-2, 0)
2008-01-09 4:49 am
Equation of linear lines:
y-y1 = m(x-x1)
y-y1 = 7(x-x1) Slope = 7
y - (-7) = 7 (x -(-3)) Pass N(-3, -7)
y +7 = 7 (x + 3)
The point M is on x- axis. It has y coordinates 0
0 + 7 = 7x + 21
-14 = 7x
-2 = x
M(-2, 0)
y-y1 = m(x-x1)
y-y1 = 7(x-x1) Slope = 7
y - (-7) = 7 (x -(-3)) Pass N(-3, -7)
y +7 = 7 (x + 3)
The point M is on x- axis. It has y coordinates 0
0 + 7 = 7x + 21
-14 = 7x
-2 = x
M(-2, 0)
2008-01-05 9:23 am
Slope of MN=7
let (x,y) and (-3,-7) be the coordiantes of MN
(-7-y)/(-3-x)=7
-7-y=7(-3-x)
-7-y=-21-7x
7x-y=-14 equation of perpendicular line --- (1)
equation of AB
slope=-1/7
y=(-1/7)x+b
3=(-1/7)(5)+b
3=-5/7+b
b=3+5/7=26/7
y=(-1/7)x+26/7
y+x/7=26/7
x+7y=26 --- (2)
solve (1) and (2), you get (x,y) coordinates of M.
let (x,y) and (-3,-7) be the coordiantes of MN
(-7-y)/(-3-x)=7
-7-y=7(-3-x)
-7-y=-21-7x
7x-y=-14 equation of perpendicular line --- (1)
equation of AB
slope=-1/7
y=(-1/7)x+b
3=(-1/7)(5)+b
3=-5/7+b
b=3+5/7=26/7
y=(-1/7)x+26/7
y+x/7=26/7
x+7y=26 --- (2)
solve (1) and (2), you get (x,y) coordinates of M.
2008-01-05 9:08 am
If M is (h, 0) and AB perp tp MN then
{7/(h+3)}{(4--3)/(--2--5)} = -- 1
whence h = --2 then M is (--2, 0).
{7/(h+3)}{(4--3)/(--2--5)} = -- 1
whence h = --2 then M is (--2, 0).
2008-01-05 9:02 am
the equation for the line MN is
y+7=7(x+3)
and M is on the x axis so y=0
7=7(x+3)
x=-2
so M(-2,0)
y+7=7(x+3)
and M is on the x axis so y=0
7=7(x+3)
x=-2
so M(-2,0)
2008-01-05 8:58 am
It's on the x-axis so y = 0
(x,0) is the coord.
Slope = (y2-y1)/(x2-x1)
= (-7-0)/(-3-x)
= -7/(-3-x)
x = -2
M = (-2,0)
(x,0) is the coord.
Slope = (y2-y1)/(x2-x1)
= (-7-0)/(-3-x)
= -7/(-3-x)
x = -2
M = (-2,0)
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