Question

m1/m2 = x-x1/x2-x substituting these values​

Answer 1

Answer:

Draw AR, PS and BT perpendicular to the x-axis. Draw AQ and PC parallel to the x-axis. Then, by the AA similarity criterion,

Δ PAQ ~ Δ BPC

Therefore, PA/BP = AQ/PC = PQ/BC (1)

Now, AQ = RS = OS – OR = x – x1

PC = ST = OT – OS = x2 – x

PQ = PS – QS = PS – AR = y – y1

BC = BT– CT = BT – PS = y2 – y

Substituting these values in (1), we get

m1/m2 = (x − x1) / (x2 − x) = (y − y1)/(y2 − y)

Taking m1/m2 = (x − x1) / (x2 − x) , we get x = (m1x2 + m2x1)/(m1 + m2)

Similarly, taking m1/m2 = (y − y1)/(y2 − y), we get y = (m1y2 + m2y1)/(m1 + m2)

So, the coordinates of the point P(x, y) which divides the line segment joining the points A(x1, y1) and B(x2, y2), internally, in the ratio m1 : m2 are

[(m1x2 + m2x1)/(m1 + m2)] , [(m1y2 + m2y1)/(m1 + m2