If RS=ST=19, s<r and t=7, find s and r.If r=-12, s=10, and S is the midpoint of RT, find t.
To find the values of s and r, we can start by using the information given:
1. RS = ST = 19: This means that the lengths of RS and ST are both 19 units.
2. s < r: This implies that the value of s is less than the value of r.
3. t = 7: This states that the value of t is equal to 7.
If s = 10 and r = -12, we can see that r = -12 is not greater than s = 10, which contradicts the condition s < r. Therefore, the given values of s and r do not satisfy the condition.
Now, let's move on to the second part of the question. We are given that R = -12, S = 10, and S is the midpoint of RT. To find the value of t, we can use the midpoint formula.
The midpoint formula states that the coordinates of the midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) are:
(x, y) = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
In this case, let's assume that the coordinates of point T are (x, y). Given that S is the midpoint between R and T, we can set up the following equations:
(x + (-12)) / 2 = 10 (for x-coordinate)
(y + y) / 2 = 7 (for y-coordinate)
Simplifying these equations, we get:
(x - 12) / 2 = 10 => x - 12 = 20 => x = 32
(2y) / 2 = 7 => y = 7
Therefore, the coordinates of point T are (32, 7), which means that the value of t is 7.