Everything on COORDINATE SYSTEM & GEOMETRIC TRANSFORMATIONS

Identify how each vertex of triangles ABC translates to A'B'C', determine the translation vector, and verify that distances and angles stay preserved through left and right and up/down coordinate shifts.

Translate polygons by specified vectors, locate A', B', C', and E' in the new positions, and show that the translated shapes remain congruent and form a rigid transformation.

Explore rotating a shape by defining the rotation for each vertex, showing that a rigid transformation preserves distance and angle, with all points rotating by 45 degrees.

Identify the rotation point by drawing lines from original to rotated positions; their intersection yields center for 180-degree rotations, and perpendiculars at midpoints locate center and angle for non-180-degree rotations.

Identify the point of rotation by joining positions, drawing midpoints and perpendiculars to locate the intersection, then measure the counterclockwise angle of rotation from that point.

Explore how a shape achieves symmetry by reflecting over the x axis and y axis, producing a mirrored figure with corresponding points A', B', C' and distances from the axes.

Explore symmetry of shapes by performing reflections over the y axis and x axis. Learn to reflect each point, derive new coordinates, and join points to obtain the reflected polygon.

Explore reflections of a shape over the y-axis and x-axis, with point-by-point coordinates shown in prime notation, illustrating symmetry in coordinate systems and geometric transformations.

Demonstrate resizing a polygon via dilation by factors two and one half, multiplying coordinates by two or by half, plotting new points, and joining them to compare with the original.

Apply dilation by 1.5 and shrinkage by 0.5 to a polygon about the origin, compute the new vertex coordinates, and plot the resized shapes.

This lecture shows resizing a shape by dilation about the origin, using scale factors 1.25 and 0.25, by multiplying coordinates and noting distances change.