Question

Point J(5, -9) is the midpoint of HI. If H is located at (2, -6), what are the coordinates of I?

(A) (8, -12)
(B) (3.5, -7.5)
(C) (-1, -13)
(D) (6, -3)

Answer 1

The coordinates of point I are found using the midpoint formula and the given coordinates of points H and J. By setting up equations and solving for the unknown coordinates of I, it is determined that the coordinates are (8, -12), which aligns with option (A).

Step-by-step explanation:

The question involves finding the coordinates of point I given that point J is the midpoint of line segment HI, and the coordinates of point H are known. Because J is the midpoint, the coordinates of J are the averages of the coordinates of H and I. We can set up equations to find the coordinates of I using the midpoint formula:

If J(5, -9) is the midpoint, then:

• The x-coordinate of J is (xH + xI) / 2
• The y-coordinate of J is (yH + yI) / 2

If the coordinates of H are (2, -6), we have:

• 5 = (2 + xI) / 2
• -9 = (-6 + yI) / 2

Solving for xI and yI, we obtain:

• xI = 2*5 - 2 = 8
• yI = 2*(-9) + 6 = -12

Therefore, the coordinates of I are (8, -12), which corresponds to option (A).