Answer:
R(-7,0)
Explanation:
Let the midpoint of PR be Q(-1,3) where P is (5,6). To get the other coordinate R, we will use the midpoint formula as shown;
Q(X,Y) = {(x₁+x₂)/2, (y₁+y₂)/2}
From the formula;
X = (x₁+x₂)/2 and Y = (y₁+y₂)/2
From the coordinates given, X = -1, Y = 3, x₁ = 5 and y₁ = 6. To get x₂ and y₂, we will substitute the given points into the expressions above;
To get x₂;
X = (x₁+x₂)/2
-1 = (5+x₂)/2
cross multiply
-1*2 = 5+x₂
-2 = 5+x₂
subtract 5 from both sides
-2-5 = 5+x₂-5
x₂ = -7
Similarly to get y₂
Y = (y₁+y₂)/2
3 = (6+y₂)/2
cross multiply
3*2 = 6+y₂
6 = 6+y₂
subtract 6 from both sides
6-6 = 6+y₂-6
y₂ = 0
Hence the coordinate of R(x₂, y₂) is (-7,0)