The coordinates of point T are ​(0​,3​). The midpoint of ST is ​(2​,−4​). Find the coordinates of point S.

Answer 1

Your question requires the midpoint formula: Midpoint = (x₁+x₂)/2, (y₁,y₂)/2

Given that we know the midpoint, and the coordinates of one point but not the other, we can solve for the coordinates by plugging in what we know

The coordinates of point T are ​(0​,3​). The midpoint of ST is ​(2​,−4​)

Midpoint [x_m,y_m] = [(x₁+x₂)/2, (y₁₊y₂)/2]

1. We can break up the midpoint formula to solve for our missing x and y
2. x_{m =} (x₁+x₂)/2,
3. y_{m =} (y₁₊y₂)/2
4. Substitute our known values Midpoint (2,-4) and the second point T (0,3) to solve for the first point S
5. 2 = (x₁+0)/2
6. 2 = x/2
7. x = 4
8. -4= (y₁+3)/2
9. -8 = y + 3
10. y = -11
11. Therefore the coordinates of point S are (4,-11)

Answer 2

The midpoint coordinates ST(x_ST,y_ST) are given by the mean of the coordinates of the two points T(x_T, y_T) and S(x_S, y_S).

So, it means that x_ST = (x_T+x_S)/2

and y_ST = (y_T+y_S)/2

Therefore, we can find x_S and y_S

x_S = 2*x_ST-x_T = 4

y_S = 2*y_ST-y_T = -11

So, the point S has coordinates (4, -11)