Triangle MNO has vertices with coordinates (–8, 2), (–5, 5), and (5, – 2).





Which of these equations represents the line that passes through point N and is perpendicular to the line passing through points O and M?
y = x + 3

y = x - 3

y = -x + 3

y = -x - 3

Triangle MNO has vertices with coordinates 8 2 5 5 and 5 2Which of these equations represents the line that passes through point N and is perpendicular to the l class=

Respuesta :

Answer:

i think its c

Step-by-step explanation:

The equation of a straight line is represented as: [tex]y = mx + c[/tex]

The equation of the line is: [tex](c)\ y = -x +3[/tex]

The coordinates are given as:

[tex]M = (-5,5)[/tex]

[tex]N = (5,-2)[/tex]

[tex]O = (-8,2)[/tex]

First, we calculate the slope of line MO using:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

So, we have:

[tex]m = \frac{2-5}{-8--5}[/tex]

[tex]m = \frac{-3}{-3}[/tex]

[tex]m = 1[/tex]

The line that passes through N is perpendicular to MO.

This means that, the slope (m2) of the line is:

[tex]m_2 = -\frac 1m[/tex]

So, we have:

[tex]m_2 = -\frac 1{1}[/tex]

[tex]m_2 = -1[/tex]

The equation of the line is then calculated as:

[tex]y = m_2(x - x_1) + y_1[/tex]

Where:

[tex]m_2 = -1[/tex]

[tex]N = (5,-2)[/tex] --- [tex](x_1,y_1)[/tex]

So, we have:

[tex]y = -1(x -5) - 2[/tex]

[tex]y = -x +5 - 2[/tex]

[tex]y = -x +3[/tex]

Hence, the equation of the line is: [tex](c)\ y = -x +3[/tex]

See attachment for the graph of the lines

Read more about equations of straight lines at:

https://brainly.com/question/21627259

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