H The coordinates of the vertices for the figure HIJK are
H(0,5), (3, 3), J(4, -1), and K(1, 1).
4
1
3
2
To determine if it is a parallelogram, use the converse
of the parallelogram diagonal theorem. This states that
if the diagonals
then the
quadrilateral is a parallelogram.
1
K
-5 4 3 2
-1
2
-1
The midpoint of HJ is
is (2, 2).
and the midpoint of IK
J
2
-4
Therefore, HIJK is a parallelogram because the
diagonals
which means
they bisect each other.
-5

The correct options are;

To determine if it is a parallelogram use the converse of the parallelogram diagram diagonal theorem. This states that if the diagonals bisect each other, then the quadrilateral is a parallelogram

The midpoint of is (2, 2) and the midpoint of   is (2, 2)

Therefore, HIJK is a parallelogram because the diagonals have the same (share a common) midpoint, which means they bisect each other

Step-by-step explanation:

The given coordinates are;

H(0, 5), I(3, 3), J(4, -1), K(1, 1)

The diagonals are;

HJ and IK

The equations of the diagonals are;

Slope of segment HJ = (5 - (-1))/(0 - 4) = -3/2

Therefore, y - 5 = -3/2(x - 0)

When x = 0, y = 5, therefore c = 0 which gives;

y = -3/2x + 5

The slope of segment IK = (3 - 1)/(3 - 1) = 1

Therefore, y - 3 = x - 3

y = x

To get the intersection point, we have;

-3/2x + 5 = x

5 = 5/2x

x = 5/(5/2) = 2

y = x = 2

The coordinate of the intersection point is (2, 2)

The coordinates of the mid point if gotten from ((x₁ + x₂)/2, (y₁ + y₂)/2)

For HJ, we have;

((0 + 4)/2, (5 + (-1))/2) = (2, 2)

The coordinate of the midpoint of IK is ((3 + 1)2, (3 + 1)/2) = (2, 2)

Therefore, the diagonals bisect each other

Therefore we have;

To determine if it is a parallelogram use the converse of the parallelogram diagram diagonal theorem . This states that if the diagonals bisect each other, then the quadrilateral is a parallelogram

The midpoint of is (2, 2) and the midpoint of   is (2, 2)

Therefore, HIJK is a parallelogram because the diagonals have a common midpoint which means they bisect each other

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).

first option

a function is a relation in which an input is paired with exactly one output.

so, let's find the right answer.

in our first option, our inputs are january, february, and march. the outputs are 30, 28, and 25. each input has it's own output. this is correct!

our second option we know is incorrect, because ms. valverade has two outputs, dogs and cats. this is not a function.

our third option is incorrect as well. the yellow square has two ouputs, the square and the triangle.

lastly, in our fourth option, we see the number 7 two times with a different output. therefore, this is not a function.

remember: each input must be paired with only one output!