1. M is the midpoint of LN and O is the midpoint of NP. This makes the triangle MNO equal to half of LNP. Then you can get this equation MO= (1/2) LP
If you insert MO = 2x +6 and LP = 8x – 20 the calculation would be: 2x+6= (1/2)( 8x-20) 2x+6= 4x-10 2x-4x= -10 - 6 -2x= -16 x=8
2. Centroid is the point that intersects with three median lines of the triangle. The centroid should divide the median lines into 1:2 ratio. In AC lines, A located in the base so A.F:FC would be 1:2
Then, the answer would be: A.F= 1/(1+2) * AC A.F= 1/3 * 12= 4
FC= 2/(1+2) * AC FC= 2/3 * 12= 8
3. Since ∠BAD=∠DAC ∠ABD=∠ACD AD=AD The triangle ABD and ACD are similar. You can get this equation BD=DC x+8= 3x+12 x-3x= 12-8 -2x=4 x=-2
DC=3x+12= 3(-2) +12= 6
4. Orthocenter made by intersection of triangle altitude A BC lines slope would be (-4)-(-1)/1-4= -3/-3= 1. The altitude line slope would be -1, the function would be: y=-x +a 0= 1+a a=-1 y=-x-1 B AC lines slope would be (-4)-(-1)/1-0= -3. The altitude line slope would be 1/3, the function would be: y=1/3x+a -1=1/3(4)+a a=-7/3 y=1/3x - 7/3
C BC lines slope would be (-1)-(-1)/4 = 0/4. The line would be 0=x+a a=-1 0=x-1 x=1
5. a. Circumcenter: the intersection of perpendicular bisector lines<span> b. Incenter: the intersection of bisector lines c. Centroid: </span>the intersection of median lines<span> d. Orthocenter: </span>the intersection of altitude lines
