Answer:
YES, the value of a is 2
Explanation:
Given the coordinates F(b+1, a+2, M(3,5) and G(2a, 3b+3), if M is the midpoint of F and G then, to get the value of a and b we will use the formula for calculating the midpoint a shown;
M(X, Y) = (x₁+x₂/2, y₁+y₂/2)
X = x₁+x₂/2 and Y = y₁+y₂/2
From the given coordinates x₁ = b+1, y₁ = a+2, x₂ = 2a, y₂ = 3b+3, X = 3 and Y = 5
Substituting the given parameters into the formula, we can get the value of a and b as shown;
3 = b+1+2a/2
6 = 2a+b+1
2a+b = 5 ............... 1
Similarly, for the Y coordinate;
5 = a+2+3b+3/2
10 = a+2+3b+3
a+3b = 10-2-3
a+3b = 5 ........ 2
Solving equation 1 and 2 simulatneously using elimination method
2a+b = 5 ............... 1 * 1
a+3b = 5 ........ 2 * 2
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2a+b = 5 ...........3
2a +6b = 10.......... 4
subtract 3 from 4
b - 6b = 5-10
-5b = -5
b = -5/-5
b = 1
substitute b =1 into equation 2 to get a;
a + 3b = 5
a + 3(1) = 5
a = 5-3
a = 2
From the calculation above it is seen that the value of variable a can be determined and it is equivalent to 2