If LMN is dilated by a scale factor of 0.5, which of the following statements is not true? A. The sides of LMN are congruent to
1 answer:
Answer:
The correct option is A.
Step-by-step explanation:
Dilation represents the enlargement and compression of a figure. Whether it is an enlargement or compression, It totally depends on the scale factor.
If the absolute value of scale factor is more than 1, then it represents the enlargement and if the absolute value of scale factor is lies between 0 to 1, then it represents the compression.
Image and preimage are similar figures. It means the corresponding angles are congruent or corresponding sides are proportional.
It is given that LMN is dilated by a scale factor of 0.5.
Since scale factor is lies between 0 to 1, therefore it shows the compression.
Therefore sides of L'M'N' is smaller than LMN.
Since corresponding angles of similar figure are congruent.
So, options B, C and D represent the correct statements. Only option A represents a false statement because the sides of similar figure are proportional not congruent.
Therefore option A is correct.
You might be interested in
Answer:
A. 4".
B. Approximately 9.54".
C. Approximately 13.54".
Step-by-step explanation:
Please find the attachment.
Let x be the distance from the peak of the kite to the intersection of the diagonals and y be the distance from the peak of the kite to the intersection of the diagonals.
We have been given that two sides of a kite are 10 inches and two sides are 5 inches. The shorter diagonal is 6 inches.
A. Since we know that the diagonals of a kite are perpendicular and one diagonal (the main diagonal) is the perpendicular bisector of the shorter diagonal.
We can see from our attachment that point O is the intersection of both diagonals. In triangle AOD the side length AD will be hypotenuse and side length DO will be one leg.
We can find the value of x using Pythagorean theorem as:
Upon taking square root of both sides of our equation we will get,
Since distance can not be negative, therefore, the distance from the peak of the kite to the intersection of the diagonals is 4 inches.
B. We can see from our attachment that point O is the intersection of both diagonals. In triangle DOC the side length DC will be hypotenuse and side length DO will be one leg.
We can find the value of y using Pythagorean theorem as:
Upon substituting our given values we will get,
Upon taking square root of both sides of our equation we will get,
Since distance can not be negative, therefore, the distance from intersection of the diagonals to the top of the tail is approximately 9.54 inches.
C. We can see from our diagram that the length of longer diagram will be the sum of x and y.
Therefore, the length of longer diagonal is approximately 13.54 inches.
