N is the in center of △ABC. Use the given information to find NS. NQ=2x NR=3x−2
1 answer:
Given that N is the incenter of △ABC, NS = 4.
<h3>What is the Incenter of a Triangle?</h3>- The incenter of a triangle is the point of concurrency of the three angle bisectors of a triangle.
- The perpendicular distances from each sides of the triangle to the incenter are equal.
Given the image where:
NQ = 2x
NR = 3x − 2
NQ = NR = NS (equidistant from the incenter)
Thus:
2x = 3x - 2
- Add like terms
2x - 3x = -2
-x = -2
x = 2
NQ = NS = 2x
- Plug in the value of x
NS = 2(2)
NS = 4
Therefore, given that N is the incenter of △ABC, NS = 4.
Learn more about the incenter on:
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is the equation of the line that is perpendicular to this line and passes through the point (6, -2)
y = 7x - 44 equation of the line that is parallel to this line and passes through the point (6, -2)
<em><u>Solution:</u></em>
<em><u>Given that line is:</u></em>
y = 7x - 9
<em><u>The equation of line in slope intercept form is given as:</u></em>
y = mx + b ------ eqn 1
Where, "m" is the slope of line and "b" is the y intercept
On comparing eqn 1 with y = 7x - 9 we get,
m = 7
<h3><u>Find the equation of the line that is perpendicular to this line and passes through the point (6, -2)</u></h3>We know that,
Product of slope of a line and slope of line perpendicular to given is always -1
Therefore,
Now find the equation of line:
Thus the equation of line perpendicular to given line is found
<h3><u>Find the equation of the line that is parallel to this line and passes through the point (6, -2)</u></h3>Slopes of parallel lines are equal
Therefore, m = 7
<em><u>Substitute m = 7 and (x, y) = (6, -2) in eqn 1</u></em>
-2 = 7(6) + b
-2 = 42 + b
b = -44
<em><u>Substitute m = 7 and b = -44 in eqn 1</u></em>
y = 7x - 44
Thus equation of line parallel to given line is found