Question

1. what does the center of dilation represent in a dilation?

a. the largest point in the figure
b. a point that determines the orientation of the figure
c. the fixed point from which a figure is scaled
d. a point where all lines of symmetry meet

1. how would failing to maintain proportional relationships when creating a scale drawing affect its accuracy?

a. the scale drawing would be smaller than expected.
b. the scale factor would remain the same, but measurements would be inaccurate.
c. the drawing would be distorted but still usable.
d. the drawing would no longer accurately represent the actual object.

1. a bridge is 300 meters wide and is being scaled down by a factor of 0.02 for a model. what is the width of the model of the bridge?

a. 6 meters
b. 4 meters
c. 5 meters
d. 7 meters

Explanation:

Question 10

To determine the correct answer, we analyze each option:

• Option a: The center of dilation is not related to the "largest point" in a figure. Dilation scales a figure, not about the size of individual points. Eliminate a.
• Option b: The center of dilation does not determine the orientation of the figure. Orientation is related to rotation or reflection, not dilation. Eliminate b.
• Option c: By definition, the center of dilation is the fixed point from which a figure is scaled (enlarged or reduced) during a dilation transformation. This matches the concept.
• Option d: The center of dilation is not related to lines of symmetry. Lines of symmetry are about mirroring, while dilation is about scaling. Eliminate d.

Analyze each option for the effect of not maintaining proportional relationships in a scale drawing:

• Option a: Failing to maintain proportionality doesn't just make the drawing smaller; it can distort it in various ways (e.g., some parts too big, some too small). Eliminate a.
• Option b: If proportional relationships are not maintained, the scale factor concept is violated—measurements and the scale factor - related proportions would be inaccurate. But the key issue is the drawing's accuracy in representing the object. However, more directly, not maintaining proportionality means the drawing won't match the actual object's proportions. But let's check other options.
• Option c: A distorted drawing due to non - proportionality is not "still usable" in terms of accurately representing the object. The purpose of a scale drawing is accurate representation, so distortion makes it inaccurate and not usable for accurate representation. Eliminate c.
• Option d: Proportional relationships are essential for a scale drawing to accurately represent the actual object. If they are not maintained, the drawing will not accurately show the object's shape and size relationships. This is the most accurate description.

Step 1: Recall the scaling formula

To find the scaled - down width, we use the formula: Scaled width = Original width×Scale factor.
The original width of the bridge is 300 meters and the scale factor is 0.02.

Step 2: Calculate the scaled width

Substitute the values into the formula: Scaled width=$300\times0.02$
$300\times0.02 = 6$ (meters)

Answer:

c. The fixed point from which a figure is scaled

Question 11