Answer :
Answer:
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 ([tex]\frac{m1x2+m2x1}{m1+m2}[/tex] , [tex]\frac{m1y2+m2y1}{m1+m2}[/tex] ).
∵ 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 = [tex]\frac{(3)(8)+(1)(4)}{3+1}[/tex] = [tex]\frac{24+4}{4}[/tex] = [tex]\frac{28}{4}[/tex]
∴ x = 7
∵ y = [tex]\frac{(3)(5)+(1)(-3)}{3+1}[/tex] = [tex]\frac{15-3}{4}[/tex] = [tex]\frac{12}{4}[/tex]
∴ y = 3
∴ The coordinates of the division point are (7, 3)