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2D Coordinate Geometry

In the 1600s, René Descartes married algebra and geometry to create the Cartesian plane.

Midpoint of a Line Segment

         

Given the line segment \( \overline{PQ} \) with \( P=(16,9) \) and \( Q=(4,3) \), the midpoint of the line segment can be expressed as \( (a,b) \). What is the value of \(a+b\)?

If \(M\) is the midpoint of \(A=(-9,8)\) and \(B=(19,-18),\) what are the coordinates of \(M?\)

Two points \(X\) and \(Y\) in the xy plane have coordinates \((12,10)\) and \((26,24)\), respectively. The midpoint of the line segment \(XY\) has coordinates \((a,b)\). What is the value of \(a+b\)?

Find the value of \(p\) such that \((–6, 14)\) is the midpoint of the points \((-9, 16)\) and \((–3, p)\).

Given the line segment \( \overline{PQ} \) with \( P=(12,34) \) and \( Q= (32, 14) \), the midpoint of the line segment can be expressed as \( (a,b) \). What is the value of \(a+b\)?

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