Answer :
The distance between the given points is 5√5 (or) 11.2 units.
Step-by-step explanation:
- The given points are A=(7,4) and B=(-3,9).
- You are asked to find the distance between these two points A and B.
The distance between the points represents the length of the line joining those two points.
To find the distance between any points, the distance formula is used.
Distance = [tex]\sqrt{(x2-x1)^{2}+(y2-y1)^{2} }[/tex]
Here, the point A (7,4) is (x1,y1) and the point B (-3,9) is (x2,y2).
Therefore, substitute x2 = -3, x1 = 7, y2 = 9 and y1 = 4 in the distance formula.
Distance = [tex]\sqrt{(-3-7)^{2}+(9-4)^{2} }[/tex]
⇒ [tex]\sqrt{(-10)^{2}+(5)^{2} }[/tex]
⇒ [tex]\sqrt{100 + 25}[/tex]
⇒ [tex]\sqrt{125}[/tex]
⇒ [tex]5\sqrt{5}[/tex]
The value of √5 is 2.24
⇒ 5 × 2.24
⇒ 11.2 units.
The distance between the given points is 5√5 (or) 11.2 units.