Geometry

1. <1 and <2 are supplementary angles. m<1 is 4y+7, and m<2 is 9y + 4. Find m<2.

Supplemental angles sum to 180°....so we have that

[4y + 7 ] + [ 9y + 4] = 180    simplify

13y + 11  = 180       subtract 11 from both sides

13y  = 169         divide both sides by 13

y  = 13

So    m < 2   =  9(13)  + 4  =  117 + 4   = 121°   

2. GI bisects

3. The midpoint of UV is (5, 11). The coordinates of one endpoint are U(3, 5). Find the coordinates of endpoint V.

We can solve this  using the midpoint formula

[ 3 + x ]  / 2  = 5       multiply both sides by 2                    [5 + y ] / 2   = 11    multiply both sides by 2

3 + x  =  10                subtract 3 from both sides               5 + y    = 22        subtract 5 from both sides

x  = 7                                                                                    y  = 17

So.... V  = ( 7, 17)

4. Find the distance between points M(6, 16) and Z(-1, 14) to the nearest tenth. 

Distance   =sqrt  [  ( -1 - 6)^2  + ( 16 - 14)^2 ]    =  sqrt [ (-7)^2 + 2^2 ]  = sqrt [ 49 + 4]  = sqrt [ 53] ≈  7.3 units