Coordinates and Transformations

≈ 35 min

Coordinates and Transformations

Coordinates locate a point on a Cartesian grid: move along the horizontal $x$ -axis first, then the vertical $y$ -axis. A transformation moves a shape without changing its size: translation slides, reflection flips and rotation turns. Record a translation as a direction and number of units so another learner can reproduce it.

Worked example

Point $A(-2,3)$ means move 2 left and 3 up. Translating it 4 units right gives $A'(2,3)$ because only the horizontal coordinate changes.

Exam method

Read $x$ first, then $y$ . 2. Draw the move with an arrow or mirror line. 3. Check that all vertices move the same way and the shape stays congruent.

For the point $(-4,2)$ , write the horizontal coordinate.

Name the transformation that slides every point the same distance and direction.

Point $(3,-1)$ is translated 5 units left. What is its new x-coordinate?

Which ordered pair means 2 right and 5 down from the origin?

$(2,-5)$

$(-2,5)$

$(5,-2)$

$(-5,2)$