Question

Help me please and i will fan and give you a medal :)

A quadrilateral has vertices (1,2), (2,-1),(1,-4) and (0,-1) what specail quadrilateral is formed by connecting the midpoints of the sides?

a.)rectangle
b.)kite
c.)trapezoid
d.)rhombus

Answer 1

@micahm can you help??

Answer 2

answers.com says

Is △TVS scalene, isosceles, or equilateral? The vertices are T(1, 1), V(9, 2) and S(5, 8).

Calculate the side lengths and see. Each side length is the distance between two vertices.
TV: √[(9-1)^2 + (2-1)^2] = √[64+1] = √65
SV: √[(9-5)^2 + (8-2)^2] = √[16+36] = √52
ST: √[(5-1)^2 + (8-1)^2] = √[16+49] = √65

Sides TV and ST are equal and side SV is different. The triangle is scalene.


A quadrilateral has vertices (5, 3), (5, –1), (–1, 3), and (–1, –1). What special quadrilateral is formed by connecting the midpoints of the sides?

Find the midpoints of the sides. In this case, that's easy because the sides are all horizontal or vertical.
(5, [3-1]/2) = (5,1)
([5-1]/2, -1) = (2, -1)
(-1, [3-1]/2) = (-1, 1)
([5-1]/2, 3) = (2, 3)

Now we can check the lengths of the sides:
√[(5-2)^2 + (-1-1)^2] = √[9+4] = √13
√[(-1-2)^2 + (-1-1)^2] = √[9+4] = √13
√[(-1-2)^2 + (3-1)^2] = √[9+4] = √13
√[(5-2)^2 + (3-1)^2] = √[9+4] = √13
All sides are equal.
Diagonals are on horizontal or vertical lines, so it's easy to see their lengths are
5 - (-1) = 6 and
3 - (-1) = 4

All four sides are equal, but the diagonals are unequal. It's a rhombus.


A quadrilateral has vertices (–10, –4), (–4, 2), (0, 2), and (6, –4). What special quadrilateral is formed by connecting the midpoints of the sides?

We have to use a more general method to find some of the midpoints this time.
Coordinates of a midpoint are the average of the corresponding coordinates of the endpoints.
([6 - 10] /2, -4) = (-2, -4)
([6 + 0]/2, [-4 + 2]/2) = (3, -1)
([0 - 4]/2, 2) = (-2, 2)
([-4 - 10]/2, [-4 + 2]]/2) = (-7, -1)

Lengths of sides:
√[(-2-3)^2 + (-4 - (-1))^2] = √[25+9] = √34
√[(-2-3)^2 + (-1-2)^2] = √[25+9] = √34
√[(-2 - (-7))^2 + (-1-2)^2] = √[25+9] = √34
√[(-7 - (-2))^2 + (-1 - (-4))^2] = √[25+9] = √34

Again, sides are the same lengths. How about the diagonals?
3 - (-7) = 10
2 - (-4) = 6
We've got another rhombus.

Answer 3

Thank you :)