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If a line passes through the midpoint of the line segment joining the points ( -3, -4) & (-5, 6) and its slope is 4/5 then the equation of the line is
- a)4x - 5y + 20 = 0
- b)4x – 5y + 11 = 0
- c)5x – 4y + 21 = 0
- d)5x + 4y + 11 = 0
Correct answer is option 'A'. Can you explain this answer?
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If a line passes through the midpoint of the line segment joining the ...
And (5, 8), what is the equation of this line?
First, we find the midpoint of the line segment joining the two points:
Midpoint = [(x1 + x2)/2, (y1 + y2)/2]
Midpoint = [(-3 + 5)/2, (-4 + 8)/2]
Midpoint = [1, 2]
The midpoint of the line segment is (1, 2).
Next, we need to find the slope of the line that passes through this midpoint. We can use the point-slope form of a line:
y - y1 = m(x - x1)
where (x1, y1) is the midpoint and m is the slope.
To find the slope, we can use the two given points:
slope = (y2 - y1)/(x2 - x1)
slope = (8 - (-4))/(5 - (-3))
slope = 12/8
slope = 3/2
Now we can plug in the values for the midpoint and slope to get the equation of the line:
y - 2 = (3/2)(x - 1)
Simplifying, we get:
y = (3/2)x - 1
Therefore, the equation of the line that passes through the midpoint of the line segment joining the points (-3, -4) and (5, 8) is y = (3/2)x - 1.
First, we find the midpoint of the line segment joining the two points:
Midpoint = [(x1 + x2)/2, (y1 + y2)/2]
Midpoint = [(-3 + 5)/2, (-4 + 8)/2]
Midpoint = [1, 2]
The midpoint of the line segment is (1, 2).
Next, we need to find the slope of the line that passes through this midpoint. We can use the point-slope form of a line:
y - y1 = m(x - x1)
where (x1, y1) is the midpoint and m is the slope.
To find the slope, we can use the two given points:
slope = (y2 - y1)/(x2 - x1)
slope = (8 - (-4))/(5 - (-3))
slope = 12/8
slope = 3/2
Now we can plug in the values for the midpoint and slope to get the equation of the line:
y - 2 = (3/2)(x - 1)
Simplifying, we get:
y = (3/2)x - 1
Therefore, the equation of the line that passes through the midpoint of the line segment joining the points (-3, -4) and (5, 8) is y = (3/2)x - 1.
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If a line passes through the midpoint of the line segment joining the ...
So we want to find the midpoint. Midpoint=([-5+-3]÷2,[6-4]÷2)=(-4,1). Then the equation of line is (y-1)=4/5(x+4). 5(y-1)=4(x+4). 5y-5=4x+16. Then ; 4x-5y+16+5=0. ie, 4x-5y+21=o
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If a line passes through the midpoint of the line segment joining the points ( -3, -4) & (-5, 6) and its slope is 4/5 then the equation of the line isa)4x - 5y + 20 = 0b)4x – 5y + 11 = 0c)5x – 4y + 21 = 0d)5x + 4y + 11 = 0Correct answer is option 'A'. Can you explain this answer?
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