Final answer:
To find the length of segment rt, we calculate the other endpoint using the midpoint formula and then use the distance formula. The length of the segment rt is the square root of 116, approximately 10.77 units.
Step-by-step explanation:
The student has asked how to find the length of segment rt when one endpoint is (-3, 4) and the midpoint is (2, 6). To find the other endpoint (let's call it T), we use the properties of the midpoint. The midpoint's coordinates are the average of the endpoints' coordinates. Since we have one endpoint R (-3, 4) and the midpoint (2, 6), we can set up equations to find the coordinates of T. Once we have the coordinates of T, we can use the distance formula to find the length of segment rt.
Let's say the coordinates of T are (x, y). The midpoint formula states:
- (x + (-3)) / 2 = 2
- (y + 4) / 2 = 6
Solving these equations gives us the coordinates of T which are (7, 8). Now, we use the distance formula to find the length of segment rt. The distance formula is:
Distance = √((x₂ - x₁)² + (y₂ - y₁)²)
Plugging in the coordinates of R (-3, 4) and T (7, 8), we get:
Distance = √((7 - (-3))² + (8 - 4)²)
Distance = √((10)² + (4)²)
Distance = √(100 + 16)
Distance = √116
Finally, we have found the length of segment rt, which is the square root of 116, or approximately 10.77 units long.