Answer:
PC = 12 units
AP = 10 units
Step-by-step explanation:
- The centroid of a triangle is the intersection of the three medians of the triangle
- Each median connecting a vertex with the midpoint of the opposite side
- The centroid divides each median into two parts, which are always in the ratio 2: 1 from the vertex
In ΔACE
∵ P is the centroid of it
∴ P divides CF the ratio 2: 1 from C
∴ PC = 2 PF
∵ PF = 6 units
∴ PC = 2(6)
∴ PC = 12 units
∵ P divides AD at the ratio 2: 1 from A
→ That means AD = 2 + 1 = 3 parts, and AP =
AD
∴ AP =
AD
∵ AD = 15 units
∴ AP = AP =
(15)
∴ AP = 10 units
Simplifying
9 + -2x = 35
Solving
9 + -2x = 35
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-9' to each side of the equation.
9 + -9 + -2x = 35 + -9
Combine like terms: 9 + -9 = 0
0 + -2x = 35 + -9
-2x = 35 + -9
Combine like terms: 35 + -9 = 26
-2x = 26
Divide each side by '-2'.
x = -13
Simplifying
x = -13