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Ahat [919]
2 years ago
10

a line has a slope of -2/3 for a pair of points on the line. Find the missing coordinate if the points are (-1,y) and (4,7)

Mathematics
1 answer:
masha68 [24]2 years ago
8 0

Answer:

The missing co-ordinate is: (-1,$ \frac{31}{3} $).

Step-by-step explanation:

Given the slope of a line and a point on it, we determine the equation of the line by slope - one point form.

Slope - one point form: (y - y₁) = m(x - x₁)

Where, (x₁,y₁) is the point passing through the line.

Here the slope is $ \frac{-2}{3} $ and the point (x₁,y₁) = (4,7).

Therefore the equation would be:

y - 7 = $ \frac{-2}{3} $(x - 4)

⇒  3y - 21 = -2x + 8

⇒                       2x + 3y - 29 = 0       is the equation of the line.

Now it is given that (-1,y) also passes through the line, this point should satisfy the equation.

⇒ 2(-1) +3y = 29

⇒ 3y = 31  i.e., y = $ \frac{31}{3} $

Therefore, the missing co-ordinate is:   (-1,$ \frac{31}{3} $).

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What is the slope of a line parallel to the line whose equation is 2. – y= -7. Fully
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Step-by-step explanation:

Hmmmmm you did not give the full equation for the original line.

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7 0
1 year ago
Please help it will help a lot i really need this!!
Lorico [155]

Answer:

A' = (0,0)

B'=(8,0)

C'=(8,2)

D'=(0,2)

It is not a rigid motion.

Step-by-step explanation:

To use the mapping rule, substitute the original x and y values in it.

The coordinates of A are (0,0).

Using the mapping rule, the x coordinate of A' = 2x0 = 0

Using the mapping rule, the y coordinate of A' = (1/2)x0=0

So A' will not change locations. The image will be at (0,0).

The coordinates of B are (4,0)

Using the mapping rule, the x-coordinate of B' = 2x4 = 8

Using the mapping rule, the y-coordinate of B' = (1/2)x0=0

Therefore the image of B' will be located at coorindate (8,0)

The coorindates of C are (4,4).

Using the mapping rule, the x-coordinate of C' = 2x4=8

Using the mapping rule, the y-coordinate of C' = (1/2)x4=2

Therefore the image of C' will be located at coordinate (8,2)

The coordinates of D are (0,4)

Using the mapping rule, the x-coordinate of D' = 2x0 = 0

Using the mapping rule, the y-coordinate of D' = (1/2)x4=2

Therefore the image of D' will be located at coordinate (0,2)

<em>Is the transformation a rigid motion?</em>

NO, this transformation is not a rigid motion because the relative distance between the points does not stay the same after they have been transformed. The transformation is not a translation , rotation, reflection, nor glide reflection.

6 0
2 years ago
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