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laiz [17]
3 years ago
15

Show why, for linear functions, a vertical translation is equivalent to a horizontal translation. For a linear function, what ho

rizontal translation is equivalent to a vertical translation of 3 units up?
Mathematics
1 answer:
V125BC [204]3 years ago
8 0

Explanation:

A) For the function ...

f(x) = mx + b

the vertical translation by k makes the function ...

g(x) = f(x) + k = mx + b + k

This can be rewritten as ...

g(x) = m(x +k/m) +b = f(x+k/m)

That is, the vertical translation by k is equivalent to a horizontal translation by -k/m, where m is the slope of the linear function.

___

B) For a vertical translation of 3, the equivalent horizontal translation is ...

-k/m for k=3

= -3/m . . . . . where m is the slope of the function

_____

Please note that there is no equivalent for m=0.

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What are the x- and y- coordinates of point P on the directed line segment from K to J such that P is Three-fifths the length of
Mrrafil [7]

Answer:

\left ( \frac{3x_2+5x_1}{8},\frac{3y_2+5y_1}{8} \right )

Step-by-step explanation:

Given: P is Three-fifths the length of the line segment from K to J

To find: x- and y-coordinates of point P on the directed line segment from K to J

Solution:

Section formula:

Let point K and J be (x_1,y_1)\,,\,(x_2,y_2) such that the point p(x,y) divides KJ in ratio m:n

Then coordinates of point  P are given by \left ( \frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n} \right )

Take m:n=3:5

So,

coordinates of point P = \left ( \frac{3x_2+5x_1}{3+5},\frac{3y_2+5y_1}{3+5} \right )=\left ( \frac{3x_2+5x_1}{8},\frac{3y_2+5y_1}{8} \right )

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3 years ago
A glass is
fenix001 [56]

Step-by-step explanation:

x=volume of the glass

(1/3)x+63=(5/8)x

63=(5/8)x-(1/3)x

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216 cm3 is the volume (answer)

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Please help me I am so confused it would mean a lot.
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Step-by-step explanation:

1. The midpoint formula says the coordinates of the midpoint are the average of the endpoints.

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y = (y₁ + y₂) / 2

I'll do #2 and #3 as examples.

2. x = (-4 + 10) / 2 = 3

y = (6 + -10) / 2 = -2

So the midpoint is (3, -2).

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y = (-8 + -4.5) / 2 = -6.25

So the midpoint is (-4.75, -6.25).

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△QRS is rotated about point P to △Q′R′S′ . Which statements are true about the pre-image and image?
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Note that rotation will not affect the shape and size of an object.

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The corresponding lengths, from the point of rotation, between the pre-image and the image are preserved

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