Answer:
To find the midpoint of two points, you use the midpoint formula:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
Given:
S(5,2) is the midpoint of R(a+2,5) and T(6,b).
Let's plug in the values we have:
For the x-coordinate:
5 = ((a + 2) + 6) / 2
5 = (a + 8) / 2
10 = a + 8
a = 2
For the y-coordinate:
2 = (5 + b) / 2
4 = 5 + b
b = -1
So, the values of a and b are:
a = 2
b = -1
Answer:
a = 2 , b = - 1
Step-by-step explanation:
calculate the midpoint of RT using the midpoint formula, then equate the x and y coordinates to the corresponding coordinates of S
• midpoint = ( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )
let (x₁, y₁ ) = R (a + 2, 5 ) and (x₂, y₂ ) = T (6, b ) , then
S = ( [tex]\frac{a+2+6}{2}[/tex] , [tex]\frac{5+b}{2}[/tex] ) = ( [tex]\frac{a+8}{2}[/tex] , [tex]\frac{5+b}{2}[/tex] )
equate corresponding x and y coordinates to S (5, 2 ), that is
[tex]\frac{a+8}{2}[/tex] = 5 ( multiply both sides by 2 )
a + 8 = 10 ( subtract 8 from both sides )
a = 2
and
[tex]\frac{5+b}{2}[/tex] = 2 ( multiply both sides by 2 )
5 + b = 4 ( subtract 5 from both sides )
b = - 1
Thus a = 2 and b = - 1
