Question

Solve using geometry

UV is (5,-11). The coordinates of one endpoint are U(3,5). Find the coordinates of endpoint V.

Answer 1

The distance between two points in a coordinate plane can be found using the distance formula:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

In this case, the distance between U(3,5) and V(x,y) is equal to the distance between U(3,5) and UV(5,-11):

√((x - 3)² + (y - 5)²) = √((5 - 3)² + (-11 - 5)²)

Simplifying:

√((x - 3)² + (y - 5)²) = √(2² + (-16)²)

√((x - 3)² + (y - 5)²) = √(4 + 256)

√((x - 3)² + (y - 5)²) = √260

Squaring both sides:

(x - 3)² + (y - 5)² = 260

Expanding:

(x - 3)(x - 3) + (y - 5)(y - 5) = 260

x² - 6x + 9 + y² - 10y + 25 = 260

x² - 6x + y² - 10y = 260 - 9 - 25

x² - 6x + y² - 10y = 226

Now we can plug in the coordinates of UV(5,-11) to find the coordinates of V:

5² - 6(5) + (-11)² - 10(-11) = 226

25 - 30 + 121 + 110 = 226

226 = 226

Therefore, the coordinates of endpoint V are (x,y) = (5,-11).