Question

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

Answer 1

Answer:

i think its c

Step-by-step explanation:

Answer 2

The equation of a straight line is represented as: $y = mx + c$

The equation of the line is: $(c)\ y = -x +3$

The coordinates are given as:

$M = (-5,5)$

$N = (5,-2)$

$O = (-8,2)$

First, we calculate the slope of line MO using:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

So, we have:

$m = \frac{2-5}{-8--5}$

$m = \frac{-3}{-3}$

$m = 1$

The line that passes through N is perpendicular to MO.

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

$m_2 = -\frac 1m$

So, we have:

$m_2 = -\frac 1{1}$

$m_2 = -1$

The equation of the line is then calculated as:

$y = m_2(x - x_1) + y_1$

Where:

$m_2 = -1$

$N = (5,-2)$ --- $(x_1,y_1)$

So, we have:

$y = -1(x -5) - 2$

$y = -x +5 - 2$

$y = -x +3$

Hence, the equation of the line is: $(c)\ y = -x +3$

See attachment for the graph of the lines

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