LM is a perpendicular bisector of NP. The length of LN is 12w+7, and the length of LP is 15w−5. What is the length of LN?

Given:

LM is a perpendicular bisector of NP.

The length of LN is 12w+7, and the length of LP is 15w−5.

To find:

The length of LN.

Solution:

All points on a perpendicular bisector of a segment are equidistant from the end points of the segment.

Since, LM is a perpendicular bisector of NP, therefore L is equidistant from N and P.

Isolate variable terms.

Divide both sides by 3.

Now,

Therefore, the length of LN is 55 units.

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form