Question

Point J is at (-2, 7) Point K is at (4, -1). What's the midpoint and length of segment JK?

a) Midpoint: (1, 3); Length: 7.81 units
b) Midpoint: (1, 3); Length: 8 units
c) Midpoint: (1, 8); Length: 7.81 units
d) Midpoint: (1, 8); Length: 8 units

Answer 1

The midpoint of segment JK is (1, 3) and the length of segment JK is 10 units.

None of the given options is correct

Step-by-step explanation:

To find the midpoint of segment JK, we use the midpoint formula. The midpoint formula states that the coordinates of the midpoint are the averages of the x-coordinates and y-coordinates of the two endpoints.

The x-coordinate of the midpoint is (-2 + 4) / 2 = 1, and the y-coordinate is (7 + -1) / 2 = 3. Therefore, the midpoint of segment JK is (1, 3).

To find the length of segment JK, we use the distance formula. The distance formula states that the length of a segment is the square root of the difference of the x-coordinates squared plus the difference of the y-coordinates squared.

The difference of the x-coordinates is 4 - (-2) = 6, and the difference of the y-coordinates is -1 - 7 = -8.

The length of segment JK is √(6^2 + (-8)^2) = √(36 + 64) = √100 = 10 units.

None of the given options is correct