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3 years ago

Find the equation of the line (0,-5) and (5,0)

Mathematics

2 answers:

atroni [7]3 years ago

8 0

Answer:

y = x-5

Step-by-step explanation:

slope: 0--5/5-0 = 1

Equation: y-y1 = m(x-x1)

y-0 = 1(x-5)

y-0 = x-5

y = x-5

liraira [26]3 years ago

7 0

I think it is 4.5 but I might be wrong

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5. Show that the following points are collinear. a) (1, 2), (4, 5), (8,9)

Irina-Kira [14]

Label the points A,B,C

A = (1,2)
B = (4,5)
C = (8,9)

Let's find the distance from A to B, aka find the length of segment AB.

We use the distance formula.

$A = (x_1,y_1) = (1,2) \text{ and } B = (x_2, y_2) = (4,5)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(1-4)^2 + (2-5)^2}\\\\d = \sqrt{(-3)^2 + (-3)^2}\\\\d = \sqrt{9 + 9}\\\\d = \sqrt{18}\\\\d = \sqrt{9*2}\\\\d = \sqrt{9}*\sqrt{2}\\\\d = 3\sqrt{2}\\\\$

Segment AB is exactly $3\sqrt{2}$ units long.

Now let's find the distance from B to C

$B = (x_1,y_1) = (4,5) \text{ and } C = (x_2, y_2) = (8,9)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(4-8)^2 + (5-9)^2}\\\\d = \sqrt{(-4)^2 + (-4)^2}\\\\d = \sqrt{16 + 16}\\\\d = \sqrt{32}\\\\d = \sqrt{16*2}\\\\d = \sqrt{16}*\sqrt{2}\\\\d = 4\sqrt{2}\\\\$

Segment BC is exactly $4\sqrt{2}$ units long.

Adding these segments gives

$AB+BC = 3\sqrt{2}+4\sqrt{2} = 7\sqrt{2}$

----------------------

Now if A,B,C are collinear then AB+BC should get the length of AC.

AB+BC = AC

Let's calculate the distance from A to C

$A = (x_1,y_1) = (1,2) \text{ and } C = (x_2, y_2) = (8,9)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(1-8)^2 + (2-9)^2}\\\\d = \sqrt{(-7)^2 + (-7)^2}\\\\d = \sqrt{49 + 49}\\\\d = \sqrt{98}\\\\d = \sqrt{49*2}\\\\d = \sqrt{49}*\sqrt{2}\\\\d = 7\sqrt{2}\\\\$

AC is exactly $7\sqrt{2}$ units long.

Therefore, we've shown that AB+BC = AC is a true equation.

This proves that A,B,C are collinear.

For more information, check out the segment addition postulate.

7 0

2 years ago

Find the value p with working

drek231 [11]

Answer:

64/672/882(986)*866772

5 0

2 years ago

Read 2 more answers

2m - 6 = 8m then 3m =

Vinil7 [7]

Answer:

3m = -3

Step-by-step explanation:

You are given

2m - 6 = 8m,

hence,

2m - 8m = 6,

-6m = 6,

m = 6%2F%28-6%29,

m = -1.

Therefore, 3m = -3.

5 0

3 years ago

Which system is equivalent to

Sergio [31]

Answer:

We can find the system equivalent to this one by replacing one of the equations with a multiply of itself, so:

Let’s multiply y = x-2 by 2

2y=2x-4

A system equivalent to this one is

y = -2x^2 (this remains the same)

2y= 2x-4

8 0

2 years ago

What is the measure of angle 2?

Darya [45]

Answer:

Step-by-step explanation:

because that angle is a little less than half of 90 so 42 is the best answer

5 0

2 years ago