Question

The coordinates of the endpoints of hi are h(–14, –11) and i(0,10). Point j is on hi and divides it such that hj:ij is 6:1. What are the coordinates of j? Write your answers as integers or decimals.

Answer 1

To find the coordinates of point j which divides the line segment hi in a 6:1 ratio, apply the section formula to the given endpoints. The coordinates of point j are (-2, 7).

Step-by-step explanation:

The student has asked a question about finding the coordinates of point j which divides the segment hi in a 6:1 ratio. The coordinates of h are (-14, -11) and i are (0,10). To find the coordinates of j, one can use the section formula which states that to divide a line segment in a given ratio, you multiply the opposite vertex coordinates by the ratio number and then add them together, followed by dividing by the sum of the ratio numbers.

For this example:

• • Find the x-coordinate of j: ((-14)*1 + 0*6) / (1+6) = (-14) / 7 = -2
  • Find the y-coordinate of j: ((-11)*1 + 10*6) / (1+6) = (-11 + 60) / 7 = 49 / 7 = 7
• Therefore, the coordinates of
• j
• are
• (-2, 7)
• .