Line segment AB has endpoints A(10, 4) and B(2, 8). Find the coordinates of the point that divides the line segment directed from A to B in the ratio of 1:4.
Mathematics · Middle School · Tue Nov 03 2020
Answered on
Given the statement:
Line segment AB has endpoints A(10, 4) and B(2, 8).
x1 = 10
x2 = 2
y1 = 4
y2 = 8
Find the coordinates of the point that divides the line segment directed from A to B in the ratio of 1:4.
Solution:
In order to find the coordinate of the point that divides the line segment, we simply need to use the midpoint formula.
Midpoint Formula:
Midpoint = ( x2 + x1 )/2, ( y2 + y1 )/2
Midpoint = ( 2 + 10 ) /2 , ( 4 + 8 )/2
Midpoint = 12/2, 12/2
Midpoint = 6, 6
Since the scale is 1:4, we multiply 6, in the y coordinate by 4.
Midpoint = (6, 24)
Final answer:
Midpoint = (6, 24)