Respuesta :
The point Q that partitions the line segment is Q(2,28)
Given that the directed line segment AB, with endpoints A(20, 6) and B(-16, 50) and divide the segment into a 1:1 ratio.
A line segment is a part of a line bounded by two distinct endpoints and containing all the points of the line segment between its endpoints.
We will find the point Q by using the section formula that is
Q(x,y)=((mx₂+nx₁)/(m+n),(my₂+ny₁)/(m+n))
The given ratio is m:n=1:1 and the points (x₁,y₁)=(20,6) and (x₂,y₂)=(-16,50).
Firstly, we will find the point Q for x-axis, we get
Q(x)=(mx₂+nx₁)/(m+n)
Q(x)=(1×(-16)+1×20)/(1+1)
Q(x)=(-16+20)/2
Q(x)=4/2
Q(x)=2
Now, we will find the point Q for y-axis, we get
Q(y)=(my₂+ny₁)/(m+n)
Q(y)=(1×50+1×6)/(1+1)
Q(y)=(50+6)/2
Q(y)=56/2
Q(y)=28
The point Q that partitions the line segment is Q(x,y)=(2,28)
Hence, point Q partitions this segment into a 1:1 ratio with directed line segment AB, with endpoints A(20, 6) and B(-16, 50) is Q(2,28).
Learn more about the line segment from here brainly.com/question/9034900
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