Question

Segment Jl has endpoint j( -3,-4) and L( 7,6). what are the coordinate of point k, so that point k is on line segment jk and jk = 3/5 jl

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Answer 1

To find the coordinates of point K on segment JL given J(-3, -4) and L(7, 6), so JK is 3/5 of JL, we use the section formula. As K divides JL in the ratio 3:2, the coordinates of K are calculated to be (3, 2).

Step-by-step explanation:

The student needs to find the coordinates of point K on segment JL so that JK is 3/5 of JL. The coordinates given are J(-3, -4) and L(7, 6). To find the coordinates of K, we use the section formula or the concept of internal division.

Let K(x, y) be the required point. We apply the section formula as follows:

• x-coordinate: x = (m×x2 + n×x1) / (m + n)
• y-coordinate: y = (m×y2 + n×y1) / (m + n)

Since JK/JL = 3/5, K divides JL in the ratio 3:2, so m = 3 and n = 2. Plugging in the values:

• x = (3×(7) + 2×(-3)) / (3 + 2) = (21 - 6) / 5 = 15 / 5 = 3
• y = (3×(6) + 2×(-4)) / (3 + 2) = (18 - 8) / 5 = 10 / 5 = 2

Therefore, the coordinates of point K are (3, 2).