What point is one-fourth the distance from A to B along segment ABfor
A(-5,3) and B(7,-5)? Thanks :)
To find a point that is one-fourth the distance from point A to point B along segment AB, we can use the distance formula and the midpoint formula.
The distance formula is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Let's calculate the distance from point A to point B:
dAB = √((7 - (-5))^2 + (-5 - 3)^2)
dAB = √((7 + 5)^2 + (-8)^2)
dAB = √(12^2 + (-8)^2)
dAB = √(144 + 64)
dAB = √208
dAB ≈ 14.422
Now, in order to find a point one-fourth the distance from point A to point B, we can use the midpoint formula:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
Let's find the midpoint of AB:
Midpoint = ((-5 + 7)/2, (3 + (-5))/2)
Midpoint = (2/2, -2/2)
Midpoint = (1, -1)
So, the midpoint of AB is (1, -1).
To find a point one-fourth the distance from point A to point B, we can use the direction from point A towards the midpoint and calculate one-fourth of the distance from A to the midpoint.
Let's calculate the one-fourth distance:
d = (1/4) * dAB
d = (1/4) * 14.422
d ≈ 3.6055
Now, we can find the point one-fourth the distance from A to B by moving from point A towards the midpoint by a distance of 3.6055 along the line AB.
To calculate the coordinates of the point, we can use the direction vector from A to the midpoint. The direction vector is (1 - (-5), -1 - 3) = (6, -4).
Now, starting from point A(-5, 3), we move 3.6055 units in the direction of the direction vector (6, -4).
The coordinates of the point one-fourth the distance from A to B along segment AB are:
x = -5 + (3.6055 * 6) ≈ 13.633
y = 3 + (3.6055 * -4) ≈ -9.422
Therefore, the point one-fourth the distance from A to B along segment AB is approximately (13.633, -9.422).