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3 years ago

The parallelogram below will undergo a single transformation.

Mathematics

2 answers:

german3 years ago

6 0

The last 2 options are correct

vladimir1956 [14]3 years ago

5 0

Answer:

The correct options are 3 and 4.

Step-by-step explanation:

The vertices of the parallelogram are P(-8,6), Q(-2,6), R(0,-3) and S(-6,3).

If a figure reflected about x = -4, then

$(x,y)\rightarrow (-x-8,y)$

Therefore the image is not identical to the original parallelogram.

If a figure reflected about y = 4.5, then

$(x,y)\rightarrow (x,-y+9)$

Therefore the image is not identical to the original parallelogram.

If a figure rotated through an angle of 360° about the origin, then

$(x,y)\rightarrow (x,y)$

Therefore the image is identical to the original parallelogram.

If a figure rotated through an angle of 360° about the vertex R, then

$(x,y)\rightarrow (x,y)$

Therefore the image is identical to the original parallelogram.

Thus the correct options are 3 and 4.

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The winery sold 81 cases of wine this week. If twice

nydimaria [60]

Answer:

Option (C)

Step-by-step explanation:

Let the red cases sold = r

and the number of white cases sold = w

Total number of cases sold by the winery = 81

r + w = 81 -------(1)

If number of red cases sold is twice of white cases sold,

r = 2w ------- (2)

By substituting the value of r from equation (2) to equation (1),

2w + w = 81

3w = 81

w = 27 cases

From equation (1),

r + 27 = 81

r = 54 cases

Therefore, number of white cases sold are 27 cases

Option (C) is he answer.

5 0

3 years ago

5. Show that the following points are collinear. a) (1, 2), (4, 5), (8,9)

Irina-Kira [14]

Label the points A,B,C

A = (1,2)
B = (4,5)
C = (8,9)

Let's find the distance from A to B, aka find the length of segment AB.

We use the distance formula.

$A = (x_1,y_1) = (1,2) \text{ and } B = (x_2, y_2) = (4,5)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(1-4)^2 + (2-5)^2}\\\\d = \sqrt{(-3)^2 + (-3)^2}\\\\d = \sqrt{9 + 9}\\\\d = \sqrt{18}\\\\d = \sqrt{9*2}\\\\d = \sqrt{9}*\sqrt{2}\\\\d = 3\sqrt{2}\\\\$

Segment AB is exactly $3\sqrt{2}$ units long.

Now let's find the distance from B to C

$B = (x_1,y_1) = (4,5) \text{ and } C = (x_2, y_2) = (8,9)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(4-8)^2 + (5-9)^2}\\\\d = \sqrt{(-4)^2 + (-4)^2}\\\\d = \sqrt{16 + 16}\\\\d = \sqrt{32}\\\\d = \sqrt{16*2}\\\\d = \sqrt{16}*\sqrt{2}\\\\d = 4\sqrt{2}\\\\$

Segment BC is exactly $4\sqrt{2}$ units long.

Adding these segments gives

$AB+BC = 3\sqrt{2}+4\sqrt{2} = 7\sqrt{2}$

----------------------

Now if A,B,C are collinear then AB+BC should get the length of AC.

AB+BC = AC

Let's calculate the distance from A to C

$A = (x_1,y_1) = (1,2) \text{ and } C = (x_2, y_2) = (8,9)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(1-8)^2 + (2-9)^2}\\\\d = \sqrt{(-7)^2 + (-7)^2}\\\\d = \sqrt{49 + 49}\\\\d = \sqrt{98}\\\\d = \sqrt{49*2}\\\\d = \sqrt{49}*\sqrt{2}\\\\d = 7\sqrt{2}\\\\$