This problem involves a dilation with scale factor k = 2, which creates an enlargement. In dilations, the scale factor determines how segment lengths change: each image segment equals the original segment multiplied by the scale factor. For triangle GHI dilated to G'H'I', we have G'H' = 2 × GH, H'I' = 2 × HI, and G'I' = 2 × GI. This means each image side is 2 times the length of the corresponding original side, confirming answer B. Students might mistakenly think k = 2 means adding 2 units (choice D), but dilations multiply lengths, not add to them. The key strategy is to recognize that scale factor k means "multiply all lengths by k" to find the image measurements.

This problem examines dilations with scale factor k = 1/2, which creates a reduction. When a figure is dilated, every segment length is multiplied by the scale factor to produce the corresponding image segment length. For quadrilateral PQRS dilated to P'Q'R'S', each image segment equals the original segment times 1/2. This means P'Q' = (1/2) × PQ, Q'R' = (1/2) × QR, and so on for all sides. Therefore, each image segment is 1/2 the length of the corresponding original segment, confirming answer A. Students might confuse this with doubling (choice B), but a scale factor less than 1 always produces a smaller image. Remember: multiply original lengths by the scale factor to find image lengths in any dilation.

This question tests finding the scale factor from given distances and applying it to segment lengths. The diagram shows OJ = 4 units and OJ' = 10 units, so the scale factor k = OJ'/OJ = 10/4 = 5/2. In a dilation, this scale factor applies to all segments, not just distances from the center. Therefore, J'K' = (5/2) × JK, which means J'K' is 5/2 as long as JK, confirming answer B. This represents an enlargement where the image is 2.5 times the original length. A common error (choice A) is to use the reciprocal 2/5, but the scale factor is always the ratio of image distance to original distance from the center. Remember: once you find the scale factor from any corresponding distances, it applies to all segment lengths in the figure.

This problem involves a dilation with scale factor k = 2/3, which creates a reduction. In any dilation, segment lengths are multiplied by the scale factor to produce image segment lengths. For triangle VWX dilated to V'W'X', we have V'W' = (2/3) × VW, W'X' = (2/3) × WX, and V'X' = (2/3) × VX. This means each image segment is 2/3 the length of the corresponding original segment, confirming answer A. Since 2/3 < 1, the image triangle is smaller than the original. A common error (choice B) is to use the reciprocal 3/2, but the given scale factor k = 2/3 directly multiplies the lengths. The misconception in choice D treats dilation as subtraction, but dilations always multiply. Apply the rule: image length = scale factor × original length.

This problem examines dilations with scale factor k = 4/3, which produces an enlargement. When a rectangle is dilated, every side length is multiplied by the scale factor to create the corresponding image side. For rectangle LMNO dilated to L'M'N'O', each image side equals the original side times 4/3. This means L'M' = (4/3) × LM, M'N' = (4/3) × MN, and so on, confirming that each image side is 4/3 times the length of the corresponding original side (answer A). Students might confuse this with the reciprocal 3/4 (choice B), but k = 4/3 means multiply by 4/3, not 3/4. The misconception in choice D treats dilation as addition rather than multiplication. To solve dilation problems correctly, always multiply lengths by the given scale factor.

This question tests understanding of how dilations with scale factor k = 3/2 affect segment lengths. In a dilation, the scale factor multiplies all distances from the center, which means each segment length is multiplied by the scale factor. Since triangle ABC is dilated to form triangle A'B'C', the corresponding segments are AB and A'B'. Applying the scale factor k = 3/2, we get A'B' = (3/2) × AB, which means A'B' is 3/2 as long as AB. This matches answer choice B, confirming that the image segment is 1.5 times the original length. A common misconception (choice A) is to think the reciprocal 2/3 applies, but dilations multiply lengths by the scale factor, not its reciprocal. To solve dilation problems, always multiply the original length by the scale factor to find the image length.

This question tests finding the scale factor from given information and applying it to segment ratios. The diagram shows OA = 5 and OA' = 3, which means the scale factor k = OA'/OA = 3/5. In a dilation, this scale factor applies uniformly to all segments in the figure. Therefore, for any corresponding segments like AB and A'B', we have A'B'/AB = k = 3/5, confirming answer B. This represents a reduction where each image segment is 3/5 the length of the original. Students might incorrectly invert the ratio (choice A), but the scale factor is always image distance divided by original distance. Once you determine k from any pair of corresponding distances from the center, that same ratio applies to all segment lengths in the dilated figure.

This problem examines a dilation with scale factor k = 5/4, which produces an enlargement. When segment MN is dilated about center O, the image segment M'N' has length equal to MN multiplied by the scale factor. Applying k = 5/4, we get M'N' = (5/4) × MN, which means M'N' is 5/4 as long as MN, confirming answer B. This represents an enlargement where the image is 1.25 times the original length. A common misconception (choice A) is to use the reciprocal 4/5, but dilations multiply by the given scale factor, not its reciprocal. Choice D incorrectly treats dilation as adding a fixed amount, but dilations are multiplicative transformations. Remember: to find image lengths in dilations, always multiply the original length by the scale factor.