Coordinate GeometryCambridge IGCSE Maths: Flashcards

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What is the order of a Cartesian coordinate pair?

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What is the order of a Cartesian coordinate pair?: $(x, y)$ — the horizontal ( $x$ ) coordinate is always given first.
State the formula for the length of a line segment between $(x_1,y_1)$ and $(x_2,y_2)$ .: $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
Find the distance between $(1,2)$ and $(4,6)$ .: $\sqrt{(4-1)^2+(6-2)^2}=\sqrt{9+16}=\sqrt{25}=5$
State the midpoint formula for $(x_1,y_1)$ and $(x_2,y_2)$ .: $\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$
Find the midpoint of $(2,-3)$ and $(8,5)$ .: $(5, 1)$
Why does the distance formula work?: It applies Pythagoras' theorem, treating the horizontal and vertical gaps between the points as the two shorter sides of a right-angled triangle.
What does it mean for three points to be collinear?: They all lie on the same straight line.
How can you check three points are collinear using coordinates?: Calculate the gradient between each pair of points; if all gradients are equal, the points are collinear.
$M(4,1)$ is the midpoint of $A(2,-3)$ and $B$ . Find $B$ .: $B = (6, 5)$ , found by rearranging the midpoint formula for each coordinate.
A common mistake when finding a midpoint is...: Subtracting the coordinates instead of adding them before dividing by 2.
Why must coordinate geometry questions on this platform be solved algebraically?: Because the exam format never includes a diagram to read values from — every answer must come from calculation.
If a line segment has length 0, what does that tell you about the two points?: The two points are the same point (identical coordinates).
Find the length of the segment joining $(0,0)$ and $(3,4)$ .: $\sqrt{3^2+4^2}=\sqrt{25}=5$
What two calculations does the midpoint formula perform?: It averages the two $x$ -coordinates and averages the two $y$ -coordinates.
$A(1,1)$ , $B(3,5)$ , $C(5,9)$ — are they collinear? Show why.: Yes: gradient $AB = 2$ and gradient $BC = 2$ , so all three points lie on the same line.