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2D Coordinate Geometry

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

Determining Coordinates

         

\(ABC\) is a right triangle with \( \angle ABC = 90 ^ \circ \).

If \( A = ( 4, 9 ) \) and \( B = ( 11, 14) \), which of the following is a possible coordinate for \(C\)?

The point \( P:(4, -26) \) is reflected across the origin, and now becomes the point \( P':(a,b) \).

What is \( a + b \)?

3 out of 4 vertices of a square have coordinates \( ( 5, 6), (5, 9) \) and \( (8, 6 ) \). What is the coordinate of the last vertex?

\(ABCD\) is a parallelogram. If \( A = (0,0) \), \( B = ( 4, 9 ) \), and \( C = ( 10, 14 ) \), what are the coordinates of \( D \)?

\(ABCD\) is a quadrilateral such that \(AB \parallel CD \). \(A = (0,0)\), \(B = (2, 9)\), \(C = ( 13, 20 ) \), which of the following is a possible coordinate of \(D\)?

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