Consider quadrilateral LMNO. If quadrilateral LMNO is a parallelogram, what must the measure of angle LMN be? m∠LMN = °
2 answers:
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Answer: The co-ordinates of F are (4.4, -4.6) and the co-ordinates of D are (4.4, -1.4).
Step-by-step explanation: Given that a square is constructed on side AD of quadrilateral ABCD such that FA lies on AB as shown in the figure. The co-ordinates of A are (6, -3) and the co-ordinates of B are (10, 1).
Also, AD : AB = 2 : 5 and the co-ordinates of the point E are (2.8, -3).
We are to select the correct co-ordinates of the points F and D.
Let, (a, b) are the co-ordinates of F and (c, d) are the co-ordinates of D.
Since ADEF is a square, so we have
AD = DE = EF = FA.
Given that
AD : AB = 2 : 5, so FA : AB = 2 : 5.
That is, \left(\dfrac{c+4.4}{2},\dfrac{d-4.6}{2}\right)=\left(\dfrac{2.8+6}{2},\dfrac{-3-3}{2}\right)
We have, after applying the internal division formula that
So, the co-ordinates of F are (4.4, -4.6).
Now, since ADEF is a square, and the diagonals of a square bisect each other.
So, the mid-points of both the diagonals are same.
That is,
So, the co-ordinates of D are (4.4, -1.4).
Thus, the co-ordinates of F are (4.4, -4.6) and the co-ordinates of D are (4.4, -1.4).
Answer:
This is possible.
Step-by-step explanation:
We can say that m<E=m<E, because of the Reflexive Property
Then, we have angles JKL and ELJ, which are equal through the peripheral angle theorem.
With these two angles, we can say that triangles ELK and EJL are similar, by the Angle-Angle Postulate (AA).
Then we can create this ratio through the Corresponding Parts of Similar Triangles Theorem, (CPST), .
With this ratio, we can cross multiply to get the desired result
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Hope this helps with your RSM problem
Yup, i caught ya.