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Part 1
A dilation maps Upper DeltaUpper QUpper RUpper S onto Upper DeltaUpper Q primeUpper R primeUpper S prime. Find the missing values.
Upper QUpper Requals7 in
Upper Q primeUpper R primeequals56 in
Upper RUpper Sequals9 in
Upper R primeUpper S primeequals__ in
Upper QUpper Sequals4 in
Upper Q primeUpper S primeequals__ in
To find the missing values, we need to identify the scale factor between the corresponding sides of the two triangles.
The scale factor, k, can be found by comparing the lengths of corresponding sides of the two triangles. The scale factor is calculated by dividing the length of the corresponding side of the image triangle by the length of the corresponding side of the original triangle.
For side QR:
k = QR'/QR = 56/7 = 8
Now, we can use the scale factor to find the missing values:
RS' = k * RS = 8 * 9 = 72 in
QS' = k * QS = 8 * 4 = 32 in
Therefore, RS' = 72 in and QS' = 32 in.