Find the coordinates of the point which divides internally the line joining the points of (8.9) and (-7,4) in the ratio 2:3
divide the line up into five equal pieces
length of each x piece = (8- -7)/5 = 15/5 = 3
length of each y piece = (9-4)/5 = 5/5 = 1
so now answer depends on if you are going two pieces from the left or the right.
If moving 2/5 of the way right from (-7 ,4)
x = -7 + 2*3 = -1
y = 4 + 2*1 = 6
so that would be at (-1,6)
(8,9), (x,y), (-7,4).
x-8 = 2/3(-7-8).
x = -2.
y-9 = 2/3(4-9).
Y = 17/3 = 5 2/3.
post it.
To find the coordinates of the point that divides the line segment internally in the given ratio, we can use the section formula.
The section formula states that if we have two points A(x₁, y₁) and B(x₂, y₂) dividing the line segment in a ratio of m₁ : m₂, then the coordinates of the point dividing the line segment internally are given by:
x = (m₁ * x₂ + m₂ * x₁) / (m₁ + m₂)
y = (m₁ * y₂ + m₂ * y₁) / (m₁ + m₂)
In this case, the coordinates of point A are (8, 9) and the coordinates of point B are (-7, 4). The ratio is given as 2:3, which means m₁ = 2 and m₂ = 3.
Now, we can substitute the values into the section formula to find the coordinates of the desired point:
x = (2 * (-7) + 3 * 8) / (2 + 3)
y = (2 * 4 + 3 * 9) / (2 + 3)
Simplifying the equations:
x = (-14 + 24) / 5
y = (8 + 27) / 5
x = 10 / 5
y = 35 / 5
x = 2
y = 7
Therefore, the point that divides the line segment internally in the ratio 2:3 is (2, 7).