ABC is an isosceles right triangle in which has a slope of -1 and mABC = 90°. ABC is dilated by a scale factor of 1.8 with the o
2 answers:
Answer:
The slope is -1
Step-by-step explanation:
Given ABC is an isosceles right triangle in which has a slope of -1 and mABC = 90°. Now, ABC is dilated by a scale factor of 1.8 with the origin as the center of dilation, resulting in the image A'B'C'.
As we know that the slope is equal to
And also in dilation only the the length of sides increases or decreases by same factor which results in same angle i.e tan remains same.
Hence, slope never changes in dilation.
Therefore, slope is -1
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Refer to the attachment for the diagram of the problem.
Let us call the two identical sides of the isosceles triangle with s. Since we know that the hypotenuse measures 45 inches, we can find s by using the Pythagorean Theorem:
We can notice that the figure will have similar triangles with the smaller triangle having one length equal to 5x. We then compute for the equivalent hypotenuse of the smaller triangle (denoted as y).
We can then solve for the value of x by applying the Pythagorean Theorem in the smaller triangle.
We ignore the negative value since there is no negative side. x is therefore 4.55 thus the dimensions of the rectangle would be 22.75 and 9.1. For the other case, the dimensions would simply be inverted since we would be dealing with a rectangle with its width longer than its length.
Let us call the two identical sides of the isosceles triangle with s. Since we know that the hypotenuse measures 45 inches, we can find s by using the Pythagorean Theorem:
We can notice that the figure will have similar triangles with the smaller triangle having one length equal to 5x. We then compute for the equivalent hypotenuse of the smaller triangle (denoted as y).
We can then solve for the value of x by applying the Pythagorean Theorem in the smaller triangle.
We ignore the negative value since there is no negative side. x is therefore 4.55 thus the dimensions of the rectangle would be 22.75 and 9.1. For the other case, the dimensions would simply be inverted since we would be dealing with a rectangle with its width longer than its length.