a line is 180 degrees and x is congruent to the angle on the right of 120, meaning if you find the missing angle to that angle(the one next to 120) then you'd get the answer. Knowing the line it 180 and 120 is supplementary to x. x=60.

6 0

3 years ago

What is the equation, in slope-intercept form, of the perpendicular bisector of the given line segment?

frosja888 [35]

Complete Question:

The given line segment has a midpoint at (3, 1). On a coordinate plane, a line goes through (2, 4), (3, 1), and (4, -2).

What is the equation, in slope-intercept form, of the perpendicular bisector of the given line segment?

Answer:

$y = \frac{1}{3}x$

Step-by-step explanation:

From the question, we understand that the line goes through $(2, 4), (3, 1), and\ (4, -2).$

First, we calculate the slope of the above points

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

Where

$(x_1,y_1) = (2,4)$

$(x_2,y_2) = (3,1)$

$m = \frac{1 - 4}{3 - 2}$

$m = \frac{-3}{1}$

$m = -3$

Also; from the question, we understand that the line segment is perpendicular to the above points.

This slope (m2) of the line segment is calculated as:

$m_2 = -\frac{1}{m}$

Substitute -3 for m

$m_2 = -\frac{1}{-3}$

$m_2 = \frac{1}{3}$

Lastly, we calculate the equation of the line using:

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

The line segment has a midpoint at (3, 1)

So:

$y - 1 = \frac{1}{3}(x - 3)$

Open bracket

$y - 1 = \frac{1}{3}x - 1$

Add 1 to both sides

$y - 1 +1= \frac{1}{3}x - 1+1$

$y = \frac{1}{3}x$

Hence, the equation of the line segment is: $y = \frac{1}{3}x$

7 0

3 years ago

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