Find the coordinate of points which trisect the line segment joining (1,-2) and (-3,4).

To find the coordinates of points that trisect the line segment joining the points (1, -2) and (-3, 4), we need to first find the coordinates of the two trisection points.

Trisection means dividing the segment into three equal parts. So, we'll divide the line segment into three equal parts, and the coordinates of the two trisection points will be our answer.

Step 1: Find the coordinates of the first trisection point.

The first trisection point will be one-third of the way from (1, -2) to (-3, 4). To find it, we can use the following formula:

First Trisection Point (x1, y1) = (1/3) * (x1 of the first point + x1 of the second point, 1/3 * (y1 of the first point + y1 of the second point))

= (1/3) * (1 + (-3), 1/3 * (-2 + 4))

= (1/3) * (-2, 1/3 * 2)

= (-2/3, 2/3)

So, the coordinates of the first trisection point are (-2/3, 2/3).

Step 2: Find the coordinates of the second trisection point.

The second trisection point will be two-thirds of the way from (1, -2) to (-3, 4). To find it, we can use the same formula:

Second Trisection Point (x2, y2) = (2/3) * (x1 of the first point + x1 of the second point, 2/3 * (y1 of the first point + y1 of the second point))

= (2/3) * (1 + (-3), 2/3 * (-2 + 4))

= (2/3) * (-2, 2/3 * 2)

= (-4/3, 4/3)

So, the coordinates of the second trisection point are (-4/3, 4/3).

These are the coordinates of the points that trisect the line segment joining (1, -2) and (-3, 4).