Question

15. In the coordinate plane, line Li passes through (0, 6) and (-8, 0).1) Determine the measure of the acute angle that L1 forms with the X-axis.2) Determine the distance from the origin to L13) Hence, what point on L1 is nearest to the origin?

Answer 1

Part 1

we have the points (0,6) and (-8,0)

Find out the slope

m=(0-6)/(-8-0)

m=-6/-8

m=3/4

The equation of L1 is

y=(3/4)x+6

Graph the given line

see the figure below

Find out the measure of angle X

tan(X)=6/8 -----> by TOA

X=tan^-1(3/4)

X=36.87 degrees

Part 2

step1

Find out the equation of the perpendicular line to the Line L1 that passes through the origin

Remember that

If two lines are perpendicular

then

their slopes are negative reci[rocal

so

the slope of the perpendicular line to L1 is

m=-4/3

step 2

Find out the equation of the line

y=-(4/3)x

step 3

Find out the intersection point between L1 and the perpendicular line

we have the system

y=(3/4)x+6 ----------> L1

y=-(4/3)x

Solve by graphing

step 4

Find out the distance between points (-2.88,3.84) and (0,0)

Applying the formula of the distance between two points

$\begin{gathered} d=\sqrt{(0-3.84)^2+(0+2.88)^2} \\ d=4.8 \end{gathered}$

therefore

The answer Part 2 is

The distance is 4.8 units

part 3

The point in L1 nearest to the origin is the point (-2.88,3.84)