+0

# Analytic Geometry

+2
280
2

1:  The square with vertices (-a, -a), (a, -a), (-a, a), (a, a) is cut by the line y = x/2 into congruent quadrilaterals. The perimeter of one of these congruent quadrilaterals divided by a equals what? Express your answer in simplified radical form.

2:  Find the equation of the line passing through the points (-3,-16) and (4,5). Enter your answer in "y = mx + b" form.

Thank you!

#1
+1

1:  The square with vertices (-a, -a), (a, -a), (-a, a), (a, a) is cut by the line y = x/2 into congruent quadrilaterals. The perimeter of one of these congruent quadrilaterals divided by a equals what? Express your answer in simplified radical form.

The length of the sides of one of the quadrilaterals will be the distances between these points :

(-a,  a)  and  (a, a)  = √ [ -a - a)^2  + ( a - a)^2]  = √ [ (-2a)^2 ]  = 2a

( a,a) and (a, a/2)  = √ [ (a - a)^2  + ( a - a/2)^2 ] = √ [ a^2/4] = a/2

( -a, a)   and ( -a, -a/2)  = √ [ (-a  - -a)^2  + ( a -  -a/2)^2 ] = √ (3/2a)^2  =  (3/2)a

( -a, -a/2)  and ( (a, a/2)  = √ [ (a - -a)^2  + (a/2 -  -a/2)^2  ] = √[ 4a^2  + a^2] = (√5 )a

So...the perimeter of the quadrilateral  divided by  a  =

[ 2a  + a/2  + (3/2a) + (√5)a ] / a   =   [  4a + (√5)a  ]  / a   =    a [ 4 + √5] / a    =  [ 4  + √5 ]  units

Note, ACG...look at the graph here when a  = 4.....verify for yourself that no matter the value of "a", the answer will be the "constant" answer found above :  https://www.desmos.com/calculator/dfrfzvd5mb

2:  Find the equation of the line passing through the points (-3,-16) and (4,5). Enter your answer in "y = mx + b" form.

Well...this one is a litle easier than the first  !!!

Slope  between the points is  [ -16 - 5 ] / [ -3  -4 ] =  -21 /  -7  = 3

So the equation of the line is :

y  = 3(x - 4)  + 5

y = 3x - 12 + 5

y  = 3x - 7   Jun 6, 2018
edited by CPhill  Jun 6, 2018
edited by CPhill  Jun 6, 2018
#2
+2