HardMathematicsHigh School (9–10)GeneralCoordinate Geometry › The Cartesian PlaneNumerical

A(-1, 1), B(3, 1) and C(4, 8) are three corners of the parallelogram ABCD.

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

$A(-1, 1)$ , $B(3, 1)$ and $C(4, 8)$ are three corners of the parallelogram $ABCD$ . Find $D$ and the area of the parallelogram.

Need a reminder? The key ideaShow

Reflection in the x-axis: $(x, y) \to (x, -y)$ . In the y-axis: $(x, y) \to (-x, y)$ . In the origin: $(x, y) \to (-x, -y)$ . Along a line parallel to an axis, a distance is the difference of one coordinate.

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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← Find the distance between each pair of points. (-7, -3) and (4, -3); (-5, 6) and (-5, -2)The point P(a, b) is reflected in the y-axis. →

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