A point pairs one input with one output

Read the horizontal coordinate first

In $(3,2)$, the first coordinate locates the point horizontally and the second locates it vertically. Enter the pair with parentheses and a comma. The point is three units right of the origin and two units up.

Enter $A=(3,2)$ to give the point a name. Open the point's style menu by holding its colored icon, then select Label.

$\displaystyle \left(3,2\right)$

Plot an unnamed point.

$\displaystyle A=\left(3,2\right)$

Name the point A.

$\displaystyle \left(4,f\left(4\right)\right)$

After defining f, plot its output at input 4.

Substitute the coordinates into the quantity the question asks for

If a solution point is $(3,2)$ and the question asks for $2x-y$, the answer is $2(3)-2=4$. Neither coordinate alone answers that question.

A point on $y=f(x)$ pairs an input with its output. An $x$-intercept has output zero; a $y$-intercept has input zero. Those meanings often matter more than the point's appearance.

Coordinates turn geometry into calculations

For $A=(1,-2)$ and $B=(7,6)$, the changes are $6$ horizontally and $8$ vertically. Their distance is $\sqrt{6^2+8^2}=10$; their midpoint is $(4,2)$.

A graph helps organize these quantities, but use the coordinate formulas for exact lengths and midpoints. Unequal axis scales can make a right angle or a circle look distorted.

Keep practicing the connected skills