Answer:
1,1
3,3
4,4
5,5
Step-by-step explanation:
see picture
Given:
M=(x1, y1)=(-2,-1),
N=(x2, y2)=(3,1),
M'=(x3, y3)= (0,2),
N'=(x4, y4)=(5, 4).
We can prove MN and M'N' have the same length by proving that the points form the vertices of a parallelogram.
For a parallelogram, opposite sides are equal
If we prove that the quadrilateral MNN'M' forms a parallellogram, then MN and M'N' will be the oppposite sides. So, we can prove that MN=M'N'.
To prove MNN'M' is a parallelogram, we have to first prove that two pairs of opposite sides are parallel,
Slope of MN= Slope of M'N'.
Slope of MM'=NN'.

Hence, slope of MN=Slope of M'N' and therefore, MN parallel to M'N'

Hence, slope of MM'=Slope of NN' nd therefore, MM' parallel to NN'.
Since both pairs of opposite sides of MNN'M' are parallel, MM'N'N is a parallelogram.
Since the opposite sides are of equal length in a parallelogram, it is proved that segments MN and M'N' have the same length.
2.42 is the answer ps.are u from k12? I am
Answer: 294√3
Explanation:
1) The described hexagon has these featrues:
a) 6 congruent equilateral triangles whose side lengths measure 14
b) height of each triangle = apotema = a
c) the area of each triangle is base × a / 2 = 14 × a / 2 = 7a
2) a is one leg of a right triangle whose other leg is 14 / 2 = 7, and the hypotenuse is 14.
3) Then you can use Pythagorean theorem fo find a:
14² = 7² + a² ⇒ a² = 14² - 7² = 147 ⇒ a = √ 147 = 7√3
4) Therefore, the area of one triangle is: 14 × 7√3 / 2 = 49√3
5) And the area of the hexagon is 6 times that: 6 × 49√3 = 294√3