MK · 8 cards

Coordinate Geometry and Graphs flashcards

8 cards with the formulas, rules and traps from this lesson. Answer in your head, then flip to check.

Fact · 1/8
What are the signs of x and y in each of the four quadrants?
Numbered counterclockwise from upper right: I (+, +), II (-, +), III (-, -), IV (+, -). A point with a zero coordinate lies on an axis, in no quadrant.
Rule · 2/8
How does reflecting a point across the x-axis or the y-axis change it?
Across the x-axis: (x, y) becomes (x, -y). Across the y-axis: (x, y) becomes (-x, y). Across the line y = x the coordinates swap.
Formula · 3/8
Distance formula between two points?
$d = (x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}$ , from the Pythagorean theorem. Look for triples like 3-4-5 or 5-12-13 to skip the square root.
Formula · 4/8
Midpoint formula, and how to find a missing endpoint?
$M = (\frac{x _{1} + x _{2}}{2}, \frac{y _{1} + y _{2}}{2})$ . If M and endpoint A are known, the other endpoint is $B = 2 M - A$ , coordinate by coordinate.
Formula · 5/8
Slope from two points?
$m = \frac{y _{2} - y _{1}}{x _{2} - x _{1}}$ , rise over run. Subtract in the same order on top and bottom.
Common trap · 6/8
What is the slope of a horizontal line versus a vertical line?
Horizontal (y = c): slope 0. Vertical (x = c): run is 0, so slope is undefined, not zero.
Term · 7/8
In y = mx + b, what do m and b represent?
m is the slope (rate of change); b is the y-intercept, the point (0, b) where the line crosses the y-axis, i.e. the value of y when x = 0.
Rule · 8/8
How do slopes of parallel and perpendicular lines compare?
Parallel lines have equal slopes (different intercepts). Perpendicular slopes are negative reciprocals: $m_{1} \times m_{2} = - 1$ , so slope 3 pairs with $- \frac{1}{3}$ .

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