Question

The straight line L, passes through the points with coordinates (6,5) and (10, 3. The straight line L2passes through the origin and has gradient -3. The lines L, and L intersect at point P. Find the coordinates of P.​

Answer 1

To find the coordinates of point P where the lines L1 and L2 intersect, we need to find the equation of both lines and solve for their intersection point.

Step-by-step explanation:

To find the coordinates of point P where the lines L1 and L2 intersect, we need to find the equation of both lines and solve for their intersection point.

First, for L1, we can find the slope (m) using the formula: m = (y2 - y1) / (x2 - x1). Substituting the coordinates (6,5) and (10,3) into the formula, we get m = (3-5) / (10-6) = -1/2.

Next, using the point-slope form of a line, we can write the equation of L1 as y - 5 = (-1/2)(x - 6). Likewise, the equation of L2 is y = -3x. We can solve these two equations simultaneously to find the intersection point P, which is (x,y).