Rectangle ABCD with coordinates A(1, 1), B(4, 1), C(4, 2), and D(1, 2) dilates with respect to the origin to give rectangle A'B'
CD'. If A'B' = 6, what is
the scale factor of the dilation?
A. 6
B. 3
C. 2
D. 1/2
E. 4
the scale factor of the dilation?
A. 6
B. 3
C. 2
D. 1/2
E. 4
1 answer:
Scale factor is a ratio. The correct option is C.
<h3>How are scale drawings formed?</h3>For a particular scale drawing, it is already specified that all the measurements' some constant scaled version will be taken. For example, let the scale be K feet to s inches.
Then it means
All feet measurements will then be multiplied by s/k to get the drawing's corresponding lengths.
The length of AB can be written as,
AB = √[(1-4)²+ (1-1)²]
AB = 3
Since the length A'B' is 6 units, therefore, the scale factor will be,
Scale factor = (Length after transformation)/(Length before transformation)
Scale factor = 6 /3 = 2
Hence, the correct option is C.
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Answer:
Construction of congruent segment: First we take the measurement of the line segment with help of marked scale or a compass, then by pointing the measurements we can get the congruent line segment.
Construction of congruent angle:
Step 1: Make two congruent segments,
Step 2: Adjust compass in a fixed length.
Step 3: Make an angle on any side of one segments with help of compass,
Step 4 : Again, make an angle on any side of the another segment with the same adjusted compass.
Construction of segment bisector,
Step 1: First place the compass on the one end of the segment,
Step 2: Adjust the compass approx to the half length of the segment,
Step 3: Draw arc above and below to the segment,
Step 4: Now, go the other end and by the same length draw two arcs by crossing the previous arcs.
Step 5: join the above and below crossed marks.
Construction of angle bisector:
Step 1: Place the compass on the vertex of the angle,
Step 2: Adjust the compass in any length,
Step 3: Make an arc in one segment of the angle and from that arc again Make an arc above the angle
Step 4: Make an arc of the same length in the another segment by the same vertex and crossed the arc made above the vertex.
Step 5: join the point of crossing and the vertex of the angle.
