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Vikentia [17]
2 years ago
7

On a coordinate grid, both point (−4, −1) and (2, 6) point are reflected across the y-axis. What are the coordinates of the refl

ected points?
A. (4, 1) and (−2, −6)
B. (−4, 1) and (−2, 6)
C. (−4, 1) and (2, −6)
D. (4, −1) and (−2, 6)
Mathematics
2 answers:
Alex777 [14]2 years ago
8 0

Answer:

Option D. (4, −1) and (−2, 6)

Step-by-step explanation:

we know that

The rule of the reflection of a point across the y-axis is equal to

(x,y) -----> (-x,y)

so

Applying the rule of the reflection

(−4, −1) -----> (4, −1)

(2, 6)----- (-2, 6)

Delicious77 [7]2 years ago
8 0

Answer:

Option D. (4, −1) and (−2, 6)

Step-by-step explanation:

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A square is constructed on side AD of quadrilateral ABCD such that FA lies on AB, as shown in the figure.
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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

\left(\dfrac{2\times 10+5\times a}{2+5},\dfrac{2\times 1+5\times b}{2+5}\right)=(6,-3)\\\\\\\Rightarrow \left(\dfrac{20+5a}{7},\dfrac{2+5b}{7}\right)=(6,-3)\\\\\\\Rightarrow \dfrac{20+5a}{7}=6,~~~~~\dfrac{2+5b}{7}=-3\\\\\\\Rightarrow 20+5a=42,~~~~\Rightarrow 2+5b=-21\\\\\\\Rightarrow 5a=22,~~~~~~~~~~\Rightarrow 5b=-23\\\\\\\Rightarrow a=4.4,~~~~~~~~~~~\Rightarrow b=-4.6.

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,

\textup{mid-point of DF}=\textup{mid-point of AE}\\\\\\\Rightarrow \left(\dfrac{c+4.4}{2},\dfrac{d-4.6}{2}\right)=\left(\dfrac{2.8+6}{2},\dfrac{-3-3}{2}\right)\\\\\\\Rightarrow \left(\dfrac{c+4.4}{2},\dfrac{d-4.6}{2}\right)=\left(\dfrac{8.8}{2},\dfrac{-6}{2}\right)\\\\\\\Rightarrow \dfrac{c+4.4}{2}=\dfrac{8.8}{2},~~~~~~\dfrac{d-4.6}{2}=-\dfrac{6}{2}\\\\\\\Rightarrow c+4.4=8.8,~~~~~\Rightarrow d-4.6=-6\\\\\Rightarrow c=4.4,~~~~~~~~~~~~\Rightarrow d=-1.4.

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).

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Answer:

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Step-by-step explanation:

A cyclist completes a journey of 500m in 22 seconds, part of the of the way at 10m/s and the remainder at 50m/s. how far does she travel at each speed? ... Let x = distance traveled at 10m/s and y = distance traveled at 50m/s. ... x+y=500. 50x+10y=11000. 50x+50y=25000. 50x+10y=11000. 40y=14000.

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Tarush is a landscape architect. For his first public project he is asked to create a small scale drawing of a garden to be plac
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Answer:

See the attached figure 2.

Step-by-step explanation:

The question is as shown at the attached figure 1.

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We need to draw the garden such that 1 unit on the grid represents 2 m.

So the scale factor is 1 unit = 2 m

base = 10 m = 10/2 = 5 units

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So, the garden on the grid will be a right triangle with base 5 units  and height 7.5 units.

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Answer:

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P = $5000,

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