Find the point which divides the segment from (-5,-4) to (6,-2) in the ratio 2:3
The two points are (11,2) units apart
so add 2/5 of that to the first one:
(-5,-4) + 2/5 (11,2)
= (-5,-4) + (4.4,0.8)
= (-0.6,-3.2)
To find the point that divides the segment in the given ratio, we can use the section formula.
The section formula states that if a line segment with endpoints (x₁, y₁) and (x₂, y₂) is divided by a point (x, y) in the ratio m:n, then the coordinates of point (x, y) can be found using the following formula:
x = (mx₂ + nx₁) / (m + n)
y = (my₂ + ny₁) / (m + n)
Let's plug in the values for the given points and the ratio:
Point A: (-5, -4)
Point B: (6, -2)
Ratio: 2:3 (m:n)
Using the formula, we can calculate the coordinates of the point that divides the segment:
x = (2 * 6 + 3 * -5) / (2 + 3) = (12 - 15) / 5 = -3/5
y = (2 * -2 + 3 * -4) / (2 + 3) = (-4 - 12) / 5 = -16/5
Therefore, the point that divides the segment from (-5, -4) to (6, -2) in the ratio 2:3 is (-3/5, -16/5).
To find the point that divides a segment in a given ratio, you can use the section formula. The section formula states that if a segment with endpoints (x1, y1) and (x2, y2) is divided in the ratio m:n, the coordinates of the point dividing the segment are given by:
(x, y) = ((mx2 + nx1) / (m + n), (my2 + ny1) / (m + n))
In this case, the segment is from (-5, -4) to (6, -2), and we want to divide it in the ratio 2:3. Let's substitute these values into the section formula:
(x, y) = ((2*6 + 3*(-5)) / (2 + 3), (2*(-2) + 3*(-4)) / (2 + 3))
Simplifying this expression:
(x, y) = ((12 - 15) / 5, (-4 - 6) / 5)
(x, y) = (-3/5, -10/5)
Simplifying the coordinates:
(x, y) = (-3/5, -2)
Therefore, the point that divides the segment from (-5, -4) to (6, -2) in the ratio 2:3 is (-3/5, -2).