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Mila [183]
3 years ago
10

If point U is reflected across the x = −3, what are the coordinates of its reflection image?

Mathematics
1 answer:
oee [108]3 years ago
8 0

Answer:

The coordinates of the image point will be [-(h + 6), k].

Step-by-step explanation:

Let the original point U has the coordinates (h,k).

Now, if point U reflects across the line x = - 3 line, which is parallel to the y-axis, then the only x-coordinate of the image point change but the y-coordinate will remains the same.

Now, the distance from line x = - 3 to the point U is (3 + h).

Hence, the distance of the image point is (3 + h) horizontally from the line x = - 3.

So, the distance of the image point from the y-axis will be [(h + 3) + 3] = h + 6

Therefore, the coordinates of the image point will be [-(h + 6), k]. (Answer)

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3 years ago
In this diagram, ABAC – AEDF. If the<br> area of ABAC = 6 in?, what is the<br> area of AEDF?
shepuryov [24]

Answer:

2.7 in²

Step-by-step explanation:

similar triangles have the same angles, and all side lengths (or other distances) of one triangle have the same scaling factor to the side lengths of the other triangle.

so, we know the relation between the 2 baselines is 2/3, as this is the factor to turn the baseline of the large triangle into the baseline of the smaller triangle.

in other words

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2 = 3 × 2/3

correct

how do we calculate the area of a triangle ?

Area = baseline × height / 2

from BAC we know

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baseline = 3

height = ?

6 = 3 × height / 2

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aha !

now, EDF has a height too that we need to calculate is Area. and this height has the same scaling factor compared to the larger triangle as the side lengths : 2/3

so, for EDF we know

Area = ?

baseline = 2

height = 4 × 2/3 = 8/3

therefore, the area is

Area = (2 × 8/3) / 2 = (16/3) / 2 = 8/3 = 2.66666... ≈ 2.7

the shirt answer would be :

we know from the 2 baselines that the scaling factor for each distance is 2/3.

for the area we need to multiply 2 distances, so that means we have to multiply both by 2/3. and so on the formula for the area we have to use 2/3 × 2/3.

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=>

Area small = Area large × 4/9 = 6 × 4/9 = 24/9 = 8/3 ≈ 2.7

3 0
3 years ago
The circle below is centered at the point (8, 4) and has a radius of length 4.
laiz [17]

Answer:

(x - 8)^2 + (y - 4)^2 = 16.

Step-by-step explanation:

The standard form can be written as:

(x - a)^2 + (y - b)^2 = r^2 where (a, b) is the center and r = the radius.

So here we have a = 8, b = 4 and r = 4.

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(x - 8)^2 + (y - 4)^2 = 16.

6 0
3 years ago
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