Question 1: If a triangle is enlarged from a point P by a scale factor of 3, and a vertex A of the original triangle is 4 units from P, what is the distance from P to the image of A after enlargement?

Answer: 12

Question 2: Construct an enlargement of a circle with radius 2 cm from a point O, with a scale factor of 4. Describe the new radius.

Answer: 8 cm

Question 3: A quadrilateral is enlarged from point P by a scale factor of 2. If one side of the original quadrilateral measures 5 units, what is the length of the corresponding side after enlargement?

Answer: 10

Question 4: Plot the graph of y=2x on the grid. Then, draw the image of this line after enlargement from the origin with a scale factor of 3.

Answer: Line y=6x

Question 5: A rectangle has a length of 6 units and width of 3 units. If it is enlarged from point Q by a scale factor of 2, what are the dimensions of the new rectangle?

Answer: 12 units by 6 units

Question 6: A triangle with vertices at A(2,3), B(4,5), and C(6,3) is enlarged from point P(0,0) with scale factor 2. Find the coordinates of the image of point B.

Answer: (8,10)

Question 7: Calculate the scale factor needed to enlarge a triangle so that a side measuring 7 units becomes 14 units after enlargement from a point.

Answer: 2

Question 8: A city map shows a park that measures 3 km by 2 km. If the map is enlarged from a point with a scale factor of 5, what are the actual dimensions of the park?

Answer: 15 km by 10 km

Question 9: Identify the common mistake in enlarging from a point: when students incorrectly measure distances after enlargement. How can this mistake be fixed?

Answer: They forget to multiply the original distance by the scale factor; fix by remembering to apply the scale factor to all distances from the point.

Question 10: A pentagon is enlarged from point R with a scale factor of 4. If one vertex of the pentagon is 3 units from R, what is the maximum possible distance from R to the enlarged vertex?

Answer: 12

Question 11: Challenge: Prove that the length of any segment from the center of enlargement to an image point is equal to the product of the original segment length and the scale factor, assuming the enlargement is from a point.

Answer: Since the enlargement from a point scales all distances from the center by the scale factor, the image point's distance from the center equals the original distance multiplied by the scale factor.