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Geometry and Measurement 6-8 / Week 10 / Build Day
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Week 10 · Dilations and Similar Figures

Build Day

Build Day: enlarge the floor plan
// The flashlight shadow: same shape, new size
⏱ about 20 min

Build Day: Enlarge the Floor Plan

Saturday at the Blueprint Table, Raven unrolls the model clubhouse floor plan. "Six by four. Let's make it one and a half times."

"Every length by 1.5," Rocket says, already reaching for the ruler. "Nine by six. The door, the window, everything."

"What do you notice about the corners?" Raven asks. "Still square," Rocket says. "A dilation keeps angles."

Nova hovers above the big grid paper, her light marking the origin corner. "Multiply the coordinates," she says.

Rocket plots (4, 0), (6, 0), (6, 4) and (4, 4) for the door, then multiplies. "(6, 0), (9, 0), (9, 6), (6, 6)."

Raven measures the new plan twice. Nova hums. "Same shape, one and a half times the size. Build Day done."

  1. A dilation stretches or shrinks a figure from a center by a scale factor k. The shape stays the same.
  2. From the origin, the rule is (x, y) to (kx, ky). Every length is multiplied by k; every angle is kept.
  3. The flashlight bulb is the center of a shadow. Bulb-to-wall divided by bulb-to-cutout gives k.
  4. Similar figures: equal matching angles, one ratio for all matching sides. A missing side is k times its match.
  5. Two equal angles make two triangles similar, because the third angles must match.
◇ ENLARGE A DRAWING WITH A GROWN-UP
Draw a simple shape on grid paper, corners on grid points. Write the coordinates of every corner.
Pick a scale factor, 2 or 1.5. Multiply every coordinate and plot the new shape on a bigger sheet.
Measure one old side and its new side. Check that new ÷ old equals your scale factor.
Take turns: one person picks a point, the other says where it lands.
For a grown-up
This week your student learned dilations, scale factors, similar figures and the angle-angle rule.
Ask them why the enlarged plan is not squashed. The answer should mention one scale factor for every length.
The flashlight points only at walls, never at eyes. Grid paper on the floor is taped down.
Safety first
Tape grid paper down so no one slips. Shoes on in the garage.
Scissors only for cutting, with a grown-up nearby.
BUILD DAY CHECK
  • Read the question.
  • Tap your answer.
The door corner (4, 4) is dilated by 1.5 from the origin. Where does it land?
The model floor is 6 units wide. Dilated by 1.5, how wide is the new floor, in units?
The model floor is 4 units deep and the new floor is 6 units deep. What is the scale factor?
One triangle has angles 45° and 45°. Another has angles 45° and 90°. Are they similar?
Draw the 6 by 4 floor plan with the door at (4, 0) to (6, 0). Then draw it dilated by 1.5.
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