The segment joining p1(-4,-7)and p2(6,9)is divided in to four equal parts find the points of division
To divide a line segment into equal parts, we need to find the coordinates of the points of division.
Step 1: Find the difference in the x-coordinates and the difference in the y-coordinates between the two points:
Δx = x2 - x1 = 6 - (-4) = 10
Δy = y2 - y1 = 9 - (-7) = 16
Step 2: Divide these differences by the number of equal parts, which in this case is 4:
Δx_part = Δx / 4 = 10 / 4 = 2.5
Δy_part = Δy / 4 = 16 / 4 = 4
Step 3: Starting from the initial point (p1), add the corresponding values of Δx_part and Δy_part for each part to find the coordinates of the points of division:
Point 1: (x1, y1) = (-4, -7)
Point 2: (x2, y2) = (-4 + Δx_part, -7 + Δy_part) = (-4 + 2.5, -7 + 4) = (-1.5, -3)
Point 3: (x3, y3) = (-4 + 2 * Δx_part, -7 + 2 * Δy_part) = (-4 + 2 * 2.5, -7 + 2 * 4) = (0, 1)
Point 4: (x4, y4) = (-4 + 3 * Δx_part, -7 + 3 * Δy_part) = (-4 + 3 * 2.5, -7 + 3 * 4) = (2.5, 5)
Therefore, the points of division that divide the line segment joining p1(-4, -7) and p2(6, 9) into four equal parts are:
Point 1: (-4, -7)
Point 2: (-1.5, -3)
Point 3: (0, 1)
Point 4: (2.5, 5)