Find the point on the line 4x+4y+5=0 which is closest to the point (−2,−3).
1 answer:
We know that
The point on the line 4x+4y+5=0 which is closest to the point (−2,−3) <span>will be located on the line perpendicular to the given line and will go through the given point
</span>
step 1
the slopes of two perpendicular lines
are
m1*m2=-1
given line
4x+4y+5=0------> 4y=-4x-5----> y=-x-1.25
m1=-1
so
m2=1
step 2
find the equation of the line with m2=1 and point (−2,−3)
y-y1=m*(x-x1)-----> y+3=(1)*(x+2)----> y=x+2-3-----> y=x-1
step 3
The point on the line 4x+4y+5=0 which is closest to the point (−2,−3) is the intersection of the line y=-x-1.25 and the line y=x-1
using a graph tool
see the attached figure
the solution is the point (-0.125,-1.125)
The point on the line 4x+4y+5=0 which is closest to the point (−2,−3) <span>will be located on the line perpendicular to the given line and will go through the given point
</span>
step 1
the slopes of two perpendicular lines
are
m1*m2=-1
given line
4x+4y+5=0------> 4y=-4x-5----> y=-x-1.25
m1=-1
so
m2=1
step 2
find the equation of the line with m2=1 and point (−2,−3)
y-y1=m*(x-x1)-----> y+3=(1)*(x+2)----> y=x+2-3-----> y=x-1
step 3
The point on the line 4x+4y+5=0 which is closest to the point (−2,−3) is the intersection of the line y=-x-1.25 and the line y=x-1
using a graph tool
see the attached figure
the solution is the point (-0.125,-1.125)
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Answer:
The solution of the system is the point (-5,4)
Step-by-step explanation:
<u><em>The question is</em></u>
Solve the system of equations
we have
-----> equation A
----> equation B
Solve the system by elimination
Multiply by 5 both sides equation B
----> equation C
Adds equation A and equation C
<em>Find the value of y</em>
substitute the value of x in any equation
therefore
The solution of the system is the point (-5,4)
Here is my answer. I hope this is helpful.
