Respuesta :
The midpoint of PQ is (1, -0.5)
The coordinates of the point 2/3 of the way from p to q are (-0.2, 0.4)
What is the midpoint of a line segment?
the midpoint is the middle point of a line segment. It is equidistant from both endpoints.
The midpoint of PQ
To calculate this, we use the midpoint formula;
(x,y) = {(x1 + x2)/2 , (y1 + y2)/2}
From the question; (x1,y1) = (-5,4) and (x2,y2) = (7,-5)
So (x,y) = (-5+7)/2 , (4-5)/2 = 2/2, -1/2 = (1,-0.5)
The coordinates of the midpoint of PQ are (1,-0.5)
What is the internal division of the line segment?
we will use here the internal division formula of the section formula;
Mathematically the coordinates can be calculated using the formula;
(x,y) = (mx2 + nx1)/m+ n , (my2 + ny1)/m + n
in this case, m = 2 and n = 3
(x1,y1) = (-5,4)
(x2,y2) = (7,-5)
So substituting these values, we have;
(x,y) = (2(7)+ 3(-5))/(2+3) , 2(-5) + 3(4)/(2+3)
(x,y) = (14 -15)/5 , (-10 + 12)/5
= (-1/5, 2/5) = (-0.2, 0.4)
Learn more about the internal division of line segment here:
https://brainly.com/question/7041827
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