(a+4b,a-b) and (a-3b,a) find the length of the line segment joining this pair of points.
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To find the length of the line segment joining the two points (a+4b, a-b) and (a-3b, a), we can use the distance formula.
The distance formula states that the distance between two points (x1, y1) and (x2, y2) is given by the equation:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
For our two points, we have:
x1 = a + 4b
y1 = a - b
x2 = a - 3b
y2 = a
Plugging in these values into the distance formula, we get:
d = sqrt((a - 3b - (a + 4b))^2 + (a - a + b)^2)
= sqrt((-3b - 4b)^2 + b^2)
= sqrt((-7b)^2 + b^2)
= sqrt(49b^2 + b^2)
= sqrt(50b^2)
= sqrt(50) * b
= 5 * sqrt(2) * b
Therefore, the length of the line segment joining the two points is 5 * sqrt(2) * b.
To find the length of the line segment joining the pair of points (a+4b,a-b) and (a-3b,a), we can use the distance formula.
The distance formula is given by:
d = √((x2-x1)^2 + (y2-y1)^2)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
For the points (a+4b,a-b) and (a-3b,a), we can let (x1, y1) be (a+4b,a-b) and (x2, y2) be (a-3b,a).
Substituting the values into the distance formula, we get:
d = √((a-3b - (a+4b))^2 + (a - (a-b))^2)
Simplifying this expression gives:
d = √((-7b)^2 + (b)^2)
Squaring the terms inside the square root gives:
d = √(49b^2 + b^2)
Combining like terms gives:
d = √(50b^2)
Taking the square root gives:
d = √(50) * b
The length of the line segment is therefore √50 times the length of b.