SOLUTION: 1.What point on x-axis is equidistance from the points(6,7) and (4,-3)? 2.Find the equations of the diagonals of a rectangle whose sides are x+1=0,x-4=0,y+1=0 and y-2=0.

Question 550800: 1.What point on x-axis is equidistance from the points(6,7) and (4,-3)?
2.Find the equations of the diagonals of a rectangle whose sides are x+1=0,x-4=0,y+1=0 and y-2=0.
Answer by mananth(16949) (Show Source): You can put this solution on YOUR website!

let Q be the point on the x axis (x,0)
Let P be (6,7)
distance PQ
d^2=((7-0)^2+(6-x)^2
d^2=49+36-12x+x^2
d^2=85-12x+x^2
Let the second point be R (4,-3)
Distance RQ=
d^2=(-3-0)^2+(4-x)^2
d^2=9+16-8x+x^2
D(RQ)=d(PQ)
square
85-12x+x^2=9+16-8x+x^2
60=4x
x=15
point Q(15,0)
CHECK
d^2(RQ)=(-3-0)^2+(4-15)^2
d^2(RQ)=9+121=130
d^2(PQ)=49+81=130
---------------
2.Find the equations of the diagonals of a rectangle whose sides are x+1=0,x-4=0,y+1=0 and y-2=0.
the lines are x=-1, y=-1, x=4, y=2
intersection points of the lines are
(-1,-1),(-1,2),(4,2),(4,-1)
Calculate the slope of the line passing through the points on the diagoinal
(-1,-1) & (4,2)
x1 y1 x2 y2
-1 -1 4 2

slope m = (y2-y1)/(x2-x1)
( 2 - -1 )/( 4 - -1 )
( 3 / 5 )
m= 3/ 5

Plug value of the slope and point ( -1 , -1 ) in
Y = m x + b
-1.00 = - 3/5 + b
b= -1 - - 3/5
b= - 2/ 5
So the equation will be
Y = 3/5 x - 2/5
m.ananth@hotmail.ca

RELATED QUESTIONS
Find the end points of the minor and major axis for the graph of the ellipse... (answered by ikleyn,MathLover1)

Find all points on the x-axis and y-axis that are 6 units from the point (4,-3). (answered by timofer)

1- Give the new coordinates if the point (4,-6) is transformed in the following manner:... (answered by stanbon)

Find all points on the x-axis that are 6 units from the point... (answered by josgarithmetic)

In a rhombus ABCD, AB is parallel to the straight line {{{x-y=5}}} and BC is parallel to... (answered by ikleyn)

Find all points on the x-axis that are 6 units from the point... (answered by ikleyn)

Question 7 (Multiple Choice Worth 1 points) Choose the best directions for graphing the (answered by solver91311)

Q.there are exactly 2 points on the ellipse {{{ x^2/a^2 + y^2/b^2=1 }}} whose distance... (answered by KMST)

I have 10 problems and I have four possible answers to all of them but I am not sure... (answered by solver91311)