find the coordinates of the point which divides the line segment joining the points (4, -3) and (8.5) in the ratio 3:1 internally

The coordinates of the division point are (7, 3)

Step-by-step explanation:

The coordinates of the point (x, y) which divides a segment with endpoints (x1, y1) and (x2, y2) at a ratio m1: m2 internally is ( , ).

∵ The line segment joining the points (4, -3) and (8, 5)

∴ x1 = 4 and x2 = 8

∴ y1 = -3 and y2 = 5

∵ The point divides the segment at ratio 3: 1

∴ m1 = 3 and m2 = 1

→ By using the rule above

∵ x = = =

∴ x = 7

∵ y = = =

∴ y = 3

∴ The coordinates of the division point are (7, 3)

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.