How can a translation and reflection be used to map HJK to LMN?
2 answers:
Answer:
The figure HJK translated upward and then reflected across the vertical line which is passes through the mid point of JN.
Step-by-step explanation:
Given information:
By SAS postulate,
Translation is a rigid transformation, it means the size and shape of the figure is same as the image but it moves from one place to another place.
The triangle LMN is slightly above than HJK ,so the figure HJK translated upward.
Now triangle HJK is mirror image of triangle LMN across the vertical line which is passes through the mid point of JN. So, the triangle reflected across the vertical line which is passes through the mid point of JN.
Therefore the figure HJK translated upward and then reflected across the vertical line which is passes through the mid point of JN.
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Answer:
(2,1)
Step-by-step explanation:
We can see that the given triangle.
The coordinates of A are (-1,5) .
The coordinates of B are (-1,-3).
The coordinates of C are (5,-3).
Distance formula:
AB= units
BC= units
AC= units
Pythagoras theorem:
Therefore,
When a triangle satisfied the Pythagoras theorem then, the triangle is right triangle.
Hence, the given triangle is a right triangle.
We know that circum-center of right triangle is the mid point of hypotenuse.
Mid-point formula:
Using this formula then, we get
Mid-point of hypotenuse AC is given by
Hence, the circum-center of triangle is (2,1).
I'm going to assume you meant to write fractions (because if are all non-negative integers, the series would clearly diverge), so that
and so on.
a. If the pattern continues as above, we would have the general term
b. Note that we can write as
The series diverges by comparison to the divergent series