Answer:
<em>A. To determine the value of a, set up and solve a system of equations in two variables. The value of a is 2</em>
Step-by-step 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 form up a simultaneous equation and get the value of a.
To determine the value of a, set up and solve a system of equations in two variables
For the X coordinates;
X = x₁+x₂/2
3 = b+1+2a/2
6 = 2a+b+1
2a+b = 5 ............... 1 * 1
For the Y coordinates;
5 = a+2+3b+3/2
cross multiply
10 = a+2+3b+3
collect like terms
a+3b = 10-2-3
a+3b = 5 ........ 2 * 2
Solving the resulting simultaneous equation to get the value of a
multiply equation 1 by 1 and 2 by 2 to have the resulting equations;
2a+b = 5 ...........3
2a +6b = 10.......... 4
subtract 3 from 4
(2a-2a)+(b - 6b) = 5-10
0-5b = -5
b = -5/-5
b = 1
substitute b =1 into equation 1 to get a;
2a + b = 5
2a + 1 = 5
2a = 5-1
2a = 4
a = 2
<em>From the calculation above it is seen that the value of variable a can be determined and it is equivalent to 2</em>
