Find the distance from the given point to the given line.
7) (4, -7) and y = -2x + 6
8) (2, 4) and y = -2x - 2
9) (-6, -3) and y = 2x + 4
10) (-2, 6) and y = -2x - 8
Best answer gets 10 points. I really need the help.
7) (4, -7) and y = -2x + 6
8) (2, 4) and y = -2x - 2
9) (-6, -3) and y = 2x + 4
10) (-2, 6) and y = -2x - 8
Best answer gets 10 points. I really need the help.
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Just find a line that's orthogonal to y and goes through the given point.
The slope of y = -2x + 6 is -2.
If m is the slope, then the orthogonal line always has the slope -1/m. So the line orthogonal to
y = -2x + 6 has the slope 1/2, or 0.5. It's gonna start with y = 0.5x......
Now it just needs to have the point (4, -7) on it. If you plug 4 into y = 0.5x,
you get y = 2. But it has to be -7.
So you just modify your line: y = 0.5x - 9. Now you need to find the point where the lines intersect:
-2x + 6 = 0.5x - 9
-2.5x = -15
x = 6.
Plug 6 into any of the two lines to get y. It should be the same for both. y = 0.5* 6 - 9 = -6
So the lines intersect at (6, -6). The distance between (4, -7) and (6, -6) is the distance you're looking for. It's essentially a line segment of which you need the lenght. You can find that using the Pythagorean Theorem:
(4, -7) - (6, -6) = (-2, -1)
--> d² = (-2)² + (-1)² = 5
--> d = √5
The distance between (4, -7) and y = -2x + 6 is √5.
The other ones go exactly the same. Just different numbers. You can do the same thing using vectors but that might be a little more complicated.
The slope of y = -2x + 6 is -2.
If m is the slope, then the orthogonal line always has the slope -1/m. So the line orthogonal to
y = -2x + 6 has the slope 1/2, or 0.5. It's gonna start with y = 0.5x......
Now it just needs to have the point (4, -7) on it. If you plug 4 into y = 0.5x,
you get y = 2. But it has to be -7.
So you just modify your line: y = 0.5x - 9. Now you need to find the point where the lines intersect:
-2x + 6 = 0.5x - 9
-2.5x = -15
x = 6.
Plug 6 into any of the two lines to get y. It should be the same for both. y = 0.5* 6 - 9 = -6
So the lines intersect at (6, -6). The distance between (4, -7) and (6, -6) is the distance you're looking for. It's essentially a line segment of which you need the lenght. You can find that using the Pythagorean Theorem:
(4, -7) - (6, -6) = (-2, -1)
--> d² = (-2)² + (-1)² = 5
--> d = √5
The distance between (4, -7) and y = -2x + 6 is √5.
The other ones go exactly the same. Just different numbers. You can do the same thing using vectors but that might be a little more complicated.
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Hmmmmmmmmmmmmmmmmmmmmmm