The coordinates of the midpoint of line PQ is \(\boxed{\left( {3,2} \right)}.\)
Further explanation:
The formula for distance between the two points can be expressed as follows,
\(\boxed{{\text{Distance}} = \sqrt {{{\left( {{x_2} - {x_1}} \right)}^2} + {{\left( {{y_2} - {y_1}} \right)}^2}} }\)
The formula for the coordinates of midpoint of two points can be expressed as follows,
\(\boxed{{\text{Coordinates of midpoint}} = \left( {\frac{{{x_1} + {x_2}}}{2},\frac{{{y_1} + {y_2}}}{2}} \right)}\)
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Explanation:
From the graph it has been observed the coordinate of point P is \(P\left( { - 2,8} \right)\) and coordinate of point Q is \(Q\left( { 8, -4} \right).\)
Consider the midpoint of side PQ as R.
Consider the midpoints of the side PQ as \(\left( {x,y} \right).\)
The midpoint between the points \(\left( { - 2,8} \right)\) and \(\left( { 8, -4} \right)\) can be obtained as follows,
\(\begin{aligned}{\text{Coordinate of R}} &= \left( {\frac{{8 - 2}}{2},\frac{{8 - 4}}{2}} \right)\\\left( {x,y} \right) &= \left({\frac{6}{2},\frac{4}{2}} \right)\\\left( {x,y} \right)&= \left({3,2} \right)\\\end{aligned}\)
The coordinates of the midpoint of line PQ is \(\boxed{\left( {3,2} \right)}.\)
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Coordinate Geometry
Keywords: Midpoint, point P, point Q, distance formula, section formula, line, line segment, coordinate geometry, PQ, quadrants.
