Math Problem Statement

Which side in the figure on the right corresponds to segment JH? What is the scale factor?

Solution

The problem asks about a scaled copy of a figure, with two polygons shown: one on the left and one on the right. Based on the image, the figure on the right is a scaled-up version of the figure on the left.

Questions:

  1. Which side in the figure on the right corresponds to segment JHJH?

In a scaled copy, corresponding sides are proportional and located similarly in both shapes. By observing the figure:

  • Segment JHJH is the bottom side of the left polygon.
  • The corresponding side in the right polygon would be segment DCDC, as it is in the same position (bottom side).
  1. What is the scale factor?

To determine the scale factor, we need to compare the lengths of corresponding sides. Let's compare the lengths of JHJH and DCDC.

  • JHJH is 2 units long (counting the grid squares).
  • DCDC is 4 units long.

The scale factor is: Scale factor=Length of DCLength of JH=42=2\text{Scale factor} = \frac{\text{Length of } DC}{\text{Length of } JH} = \frac{4}{2} = 2

Thus, the scale factor is 2.

Would you like further details or have any questions?


Here are 5 questions related to this topic:

  1. How do you verify if two shapes are scaled copies of each other?
  2. What is the relationship between the areas of two similar figures given their scale factor?
  3. If the scale factor between two figures is 3, how does this affect the perimeter?
  4. How can you find missing side lengths in a scaled figure?
  5. What is the difference between a scaled copy and a congruent figure?

Tip: When working with scaled figures, always compare corresponding sides and check that their ratios are equal.

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Math Problem Analysis

Mathematical Concepts

Geometry
Scaled Figures
Proportionality

Formulas

Scale factor = (Length of corresponding side in scaled figure) / (Length of side in original figure)

Theorems

The concept of similar triangles and proportional sides in geometric scaling.

Suitable Grade Level

Grade 6-8