Answer:
Option (2)
Step-by-step explanation:
Let the equation of the line is,
y - y' = m(x - x')
where (x', y') is a point lying on the given line.
And m = slope of the line = ![\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
Line given in the graph passes through two points (-5, -1) and (-2, -3).
Slope of the line 'm' = ![\frac{-3+1}{-2+5}](https://tex.z-dn.net/?f=%5Cfrac%7B-3%2B1%7D%7B-2%2B5%7D)
= ![-\frac{2}{3}](https://tex.z-dn.net/?f=-%5Cfrac%7B2%7D%7B3%7D)
Therefore, equation of the line passing through(-5, -1) and slope of the line =
will be,
y - (-1) = ![-\frac{2}{3}[x-(-5)]](https://tex.z-dn.net/?f=-%5Cfrac%7B2%7D%7B3%7D%5Bx-%28-5%29%5D)
![y+1=-\frac{2}{3}(x+5)](https://tex.z-dn.net/?f=y%2B1%3D-%5Cfrac%7B2%7D%7B3%7D%28x%2B5%29)
![y=-\frac{2}{3}x-\frac{10}{3}-1](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B2%7D%7B3%7Dx-%5Cfrac%7B10%7D%7B3%7D-1)
![y=-\frac{2}{3}x-\frac{13}{3}](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B2%7D%7B3%7Dx-%5Cfrac%7B13%7D%7B3%7D)
Option (2) will be the answer.
Answer:
Step-by-step explanation: What you want to do is find the grid point of each for example D is -4,-4 than you want to add those like B is 8,-6 so you would do -4+-8 and -4+-6 so you get 2,-10 for the distance of DB
Answer:
see explanation
Step-by-step explanation:
Calculate the slopes between pairs of the 3 points using the slope formula
m = ![\frac{y_{2}-y_{1} }{x_{2}-x_{1} }](https://tex.z-dn.net/?f=%5Cfrac%7By_%7B2%7D-y_%7B1%7D%20%20%7D%7Bx_%7B2%7D-x_%7B1%7D%20%20%7D)
with (x₁, y₁ ) = (- 9, 3) and (x₂, y₂ ) = (- 3, 9)
m =
=
=
= 1
Repeat with (x₁, y₁ ) = (5, 1) and (x₂, y₂ ) = (- 3, 9)
m =
=
= - 1
If lines are perpendicular then the product of their slopes = - 1 , then
1 × - 1 = -1
Thus there is a right angle between the 2 lines
Then triangle is right- angled
Answer:
The answer is
<h2>
![2 \sqrt{26} \: \: \: \: units](https://tex.z-dn.net/?f=2%20%5Csqrt%7B26%7D%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20units)
</h2>
Step-by-step explanation:
The distance between two points of a line segment can be found by using the formula
![d = \sqrt{ ({x_1 - x_2})^{2} + ({y_1 - y_2})^{2} } \\](https://tex.z-dn.net/?f=d%20%3D%20%20%5Csqrt%7B%20%28%7Bx_1%20-%20x_2%7D%29%5E%7B2%7D%20%2B%20%20%28%7By_1%20-%20y_2%7D%29%5E%7B2%7D%20%20%7D%20%5C%5C)
where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
P(-4, -2) and Q(-6, 8)
The length of the line segment is
![|PQ| = \sqrt{ ({ - 4 + 6})^{2} + ({ - 2 - 8})^{2} } \\ = \sqrt{ {2}^{2} + ({ - 10})^{2} } \\ = \sqrt{4 + 100} \\ = \sqrt{104} \: \: \: \: \: \: \: \\ = 2 \sqrt{26} \: \: \: \: \: \: \:](https://tex.z-dn.net/?f=%20%7CPQ%7C%20%20%3D%20%20%5Csqrt%7B%20%28%7B%20-%204%20%2B%206%7D%29%5E%7B2%7D%20%2B%20%20%28%7B%20-%202%20-%208%7D%29%5E%7B2%7D%20%20%7D%20%20%5C%5C%20%20%3D%20%20%5Csqrt%7B%20%7B2%7D%5E%7B2%7D%20%20%2B%20%20%28%7B%20-%2010%7D%29%5E%7B2%7D%20%7D%20%20%5C%5C%20%20%3D%20%20%5Csqrt%7B4%20%2B%20100%7D%20%20%5C%5C%20%20%3D%20%20%5Csqrt%7B104%7D%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%5C%20%20%3D%202%20%5Csqrt%7B26%7D%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20)
We have the final answer as
![2 \sqrt{26} \: \: \: \: units](https://tex.z-dn.net/?f=2%20%5Csqrt%7B26%7D%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20units)
Hope this helps you
Answer:
Most males preferred black laptops
Step-by-step explanation: