Given parallelogram LMNO with diagonals intersecting at point P. If MP = 2x + 5 and OP = 3x − 4, find OP.
−9
9
23
31
To find OP, we need to set MP and OP equal to each other since they are equal when the diagonals of a parallelogram intersect.
So, we have: 2x + 5 = 3x - 4
Rearranging the equation:
2x + 5 = 3x - 4
2x = 3x - 9
-x = -9
x = 9
Now we can plug x back into the expression for OP:
OP = 3x - 4
OP = 3(9) - 4
OP = 27 - 4
OP = 23
Therefore, OP = 23.