Question

The midpoint, M, of segment JK is (-1, 1). Point J has coordinates (3,9).

What are the coordinates of point K?

Answer 1

The coordinates of point K are (-5, -7).

Step-by-step explanation:

To find the coordinates of point K, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint between two points (x1, y1) and (x2, y2) is given by:

M = ((x1 + x2) / 2, (y1 + y2) / 2)

In this case, the coordinates of the midpoint M are (-1, 1) and the coordinates of point J are (3, 9). Plugging these values into the formula, we get:

K = ((3 + x2) / 2, (9 + y2) / 2)

Since we know that the x-coordinate of the midpoint is -1, we can solve for x2:

(3 + x2) / 2 = -1

3 + x2 = -2

x2 = -2 - 3

x2 = -5

Finally, we can substitute the value of x2 into the equation for the y-coordinate:

(9 + y2) / 2 = 1

9 + y2 = 2

y2 = 2 - 9

y2 = -7

Therefore, the coordinates of point K are (-5, -7).

Answer 2

To find the coordinates of point K, given the midpoint M and point J, use the midpoint formula. The coordinates for point K are found to be (-5, -7).

Step-by-step explanation:

The midpoint of a segment is the point that divides it into two equal parts. Given that the midpoint M of segment JK is (-1, 1) and point J is (3, 9), we can calculate the coordinates of point K using the midpoint formula.

For the midpoint M with coordinates (xm, ym) and the endpoints J (xj, yj) and K (xk, yk), the midpoint formula is:

xm = (xj + xk)/2

ym = (yj + yk)/2

Plugging in the known values, we get:

-1 = (3 + xk)/2

1 = (9 + yk)/2

By solving these equations, we find that:

xk = -1 × 2 - 3 = -5

yk = 1 × 2 - 9 = -7

Therefore, the coordinates of point K are (-5, -7).