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Question 1057109: Find the distance between the lines with the equations 3x+2y=14 and y=-3/2x-1/2
a.) Write the y-intercept of the first line, 3x+2y=14 as an ordered pair: ( , ) This will be the (x1,y1) you will use in the distance formula.
b.) Use (x1,y1) to write the equation of your perpendicular segment in slope intercept form.
c.) Give the point (x2,y2) where your perpendicular segment intersects with the second line, y=-3/2x-1/2
d.) Find the distance between (x1,y1) and (x2,y2). Round to the nearest hundredth if necessary.
There would be no limit to the amount of gratitude that would go to someone for helping me with this.
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Find the distance between the lines with the equations 3x+2y=14 and y=-3/2x-1/2
a.) Write the y-intercept of the first line, 3x+2y=14 as an ordered pair: ( , ) This will be the (x1,y1) you will use in the distance formula.
y-int is (0,7)
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b.) Use (x1,y1) to write the equation of your perpendicular segment in slope intercept form.
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The slope of the given line is -3/2. The slope of lines perpendicular is +2/3.
Use y-y1 = m*(x-x1) where m = slope and (x1,y1) is the point (0,7)
y - 7 = (2/3)*x
y = 2x/3 + 7
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c.) Give the point (x2,y2) where your perpendicular segment intersects with the second line, y=-3/2x-1/2
y = -3x/2 - 1/2
y = 2x/3 + 7
Find the intersection.
Since they both = y,
-3x/2 - 1/2 = 2x/3 + 7
Multiply by 6
-9x - 3 = 4x + 42
x = -45/13
y = 61/13
--> (-45/13,61/13) is the intersection.
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d.) Find the distance between (x1,y1) and (x2,y2). Round to the nearest hundredth if necessary.
d = sqrt(diffy^2 + diffx^2) = sqrt(30^2 + 45^2)/13
d = sqrt(2925)/13 = 15/sqrt(13)
Same answer.
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Use (0,7) and the distance formula to find the distance from the point to the line.
y=-3/2x-1/2
3x + 2y + 1 = 0 and (0,7)
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d = |Ax + By + C|/sqrt(A^2 + B^2)
d = |3*0 + 2*7 + 1|/sqrt(3^2+2^2)
d = 15/sqrt(13)
d =~ 4.16
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The other steps are not necessary.
If you need to do them, email via the TY note.
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