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Anestetic [448]
3 years ago
13

Line a is formed by using the points -1,6 and 3,-2 Line B is formed by using the point -3,0 and 5,4.What linear equations can be

used to represent each line
Mathematics
1 answer:
emmasim [6.3K]3 years ago
6 0

Answer:

y  =  -x  + 5

y  =  x/2  + 3/2

Step-by-step explanation:

First we calculate the slope as difference between coordinates

a) P₁ ( -1 , 6 )   P₂  ( 3 , 2 )

m =  Δy/Δx      ⇒  m  =  (  y₂ - y₁ ) / ( x₂ - x₁ )  ⇒  m = (2 -6 ) / (3 -(-1))

m =  -4 /4  

m = -1

Now we have:

y - y₁  = m ( x - x₁ )    ⇒  y  -  6  = (-1) ( x - (-1))

y  -  6  =  -1 * ( x + 1 )   ⇒  y  -  6  =  - x - 1

y  =  -x  + 5

In the second case

Q₁  ( -3 , 0 )  Q₂  ( 5  , 4 )

Again we calculate the slope

m  =  Δy / Δx    ⇒  m  =  ( 4 - 0 ) / ( 5 - (-3))    ⇒  m =  4 / 8   ⇒ m = 1/2

m  = 1/2  or  x = 0,5

And

y - y₁  = 1/2 ( x - x₁ )   ⇒  y  -  y₁  = 1/2 ( x - (-3))   ⇒   y  - 0 = 1/2 * x + 3/2

y  =  x/2  + 3/2

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koban [17]

Answer:

x^2 + 4x + y^2 +8y  =  0

Step-by-step explanation:

Given

A = (-1,-2)

B = (2,4)

AP:BP = 1 : 2

Required

The locus of P

AP:BP = 1 : 2

Express as fraction

\frac{AP}{BP} = \frac{1}{2}

Cross multiply

2AP = BP

Calculate AP and BP using the following distance formula:

d = \sqrt{(x - x_1)^2 + (y - y_1)^2}

So, we have:

2 * \sqrt{(x - -1)^2 + (y - -2)^2} = \sqrt{(x - 2)^2 + (y - 4)^2}

2 * \sqrt{(x +1)^2 + (y +2)^2} = \sqrt{(x - 2)^2 + (y - 4)^2}

Take square of both sides

4 * [(x +1)^2 + (y +2)^2] = (x - 2)^2 + (y - 4)^2

Evaluate all squares

4 * [x^2 + 2x + 1 + y^2 +4y + 4] = x^2 - 4x + 4 + y^2 - 8y + 16

Collect and evaluate like terms

4 * [x^2 + 2x + y^2 +4y + 5] = x^2 - 4x + y^2 - 8y + 20

Open brackets

4x^2 + 8x + 4y^2 +16y + 20 = x^2 - 4x + y^2 - 8y + 20

Collect like terms

4x^2 - x^2 + 8x + 4x + 4y^2 -y^2 +16y + 8y  + 20 - 20 =  0

3x^2 + 12x + 3y^2 +24y  =  0

Divide through by 3

x^2 + 4x + y^2 +8y  =  0

3 0
3 years ago
Write the equation that describes the line with slope = 1 and y-intercept= 5/2 in slope-intercept form.
Nonamiya [84]

Answer: y=x+5/2

Step-by-step explanation:

using the slope intercept formula, y=mx+b where m is the slope and b is the y-intercept, you can substitute the two values to get y=x+5/2. Please note that the slope, m, is one so it's not shown.

3 0
2 years ago
The red figure is congruent to the blue figure. Which choice describes a sequence of transformations in which the blue figure is
Colt1911 [192]

Answer:

  • 2. Rotate the triangle 90º clockwise about the origin and then translate it 10 units left and 9 units down.

Step-by-step explanation:

  • <em>Easy way to take one of the vertices and apply the transformations</em>

1. Rotate the triangle 90º counterclockwise about the origin and then translate it 10 units left and 9 units down.

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2. Rotate the triangle 90º clockwise about the origin and then translate it 10 units left and 9 units down.

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3. Rotate the triangle 90º counterclockwise about the origin then translate it 1 unit up.

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4. Rotate the triangle 90º clockwise about the origin then translate it 1 unit up.

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2 years ago
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