+1452 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!
+129907 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
