Question

If A(-2, 10) and B(7, -2), then the length, AB = ?

Answer 1

AB = root( (x2-x1)^2 + (y2-y1)^2 )

= root ( (7+2)^2 + (-2-10)¬2 )

= root ( 81 + 144 )

= root (125)

= 5×root(5)

:-)

Answer 2

Answer:

$\bigstar{\bold{Length\:of\:AB=15\:units}}$

Step-by-step explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• A = (-2, 10)
• B = (7, -2)

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• The length of AB

$\Large{\underline{\underline{\bf{Solution:}}}}$

→ We have to find the length of AB, that is the distance between A and B.

→ By using distance formula which is given by the equation,

  Distance formula = $\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2} }$

  where x₁ = -2, x₂ = 7. y₁ = 10, y₂ = -2

→ Substituting the values we get.

  $AB = \sqrt{(7+2)^{2}+(-2-10)^{2} }$

→ Simplifying it,

  $AB=\sqrt{9^{2}+-12^{2} }$

  $AB=\sqrt{81+144}$

  $AB=\sqrt{225}$

  $AB=15\:units$

→ Hence the length of AB is 15 units.

$\boxed{\bold{Length\:of\:AB=15\:units}}$

$\Large{\underline{\underline{\bf{Notes:}}}}$

→ The distance between two points is given by the distance formula,

   Distance formula = $\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2} }$