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## 2D Coordinate Geometry

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

# Coordinate Geometry Warmup

$$(4, 5)$$ is the midpoint between $$(2, 1)$$ and $$(x, y).$$ What is the value of $$xy?$$

A bug sitting at the point $$(1, 2)$$ moves 5 units vertically (parallel to the $$y$$-axis) and 1 units horizontally (parallel to the $$x$$-axis). Which ordered pair gives potential coordinates for the bug's new location?

The points $$A, B, C,$$ and $$D$$ form a rectangle that is twice as tall as it is wide. Given the coordinates of two of the points $$A = (2, -5),$$ and $$B = (2, 1),$$ where might another point of the rectangle ($$C$$ or $$D$$) be located?

$$Q = (x, y),$$ is a point on line segment $$BC$$ such that, comparing the lengths, $$BQ:QC = 1:3.$$ What is the value of $$x + y$$ if $$B$$ is the point (2, 2), and $$C,$$ the point (6, 14).

Circle $$C$$ has a center at $$(2, 1)$$ with a radius of 5. Which point could lie on the circle?

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