1.
The midpoint MPQ of PQ is given by (a + c /
2, b + d / 2)
2.
Let the x coordinates of the vertices of P_1 be :
x1, x2, x3,…x33
the x coordinates of P_2 be :
z1, x2, x3,…z33
and the x coordinates of P_3 be:
w1, w2, w3,…w33
3.
We are given with:
X1 + x2 + x3… + x33 = 99
We also want to find the value of w1 + w2 + w3… + w33.
4.
Now, based from the midpoint formula:
Z1 = (x1 + x2) / 2
Z2 = (x2 + x3) / 2
Z3 = (x3 + x4) / 2
Z33 = (x33 + x1) / 2
and
W1
= (z1 + z1) / 2
W2 = (z2 + z3) / 2
W3
= (z3 + z4) / 2
W13 = (z33 + z1) / 2
.
.
5.
W1 + w1 + w3… + w33 = (z1 + z1) / 2 + (z2 + z3) / 2 + (z33 + z1) / 2 = 2 (z1 + z2 + z3… + z33) / 2
Z1
+ z1 + z3… + z33 = (x1 + x2) / 2 + (x2 + x3) / 2
+ (x33 + x1) / 2
2 (x1 + x2 + x3… + x33) / 2 = (x1 + x2 +
x3… + x33 = 99
Answer: 99
