Question

Apply the Pythagorean Theorem to find the distance between points A and C.

Answer 1

Answer:

So the correct option is C )  58 units.

Also If we require Distance then l(AC) = √58 = 7.615 units

Step-by-step explanation:

Let the Points be

point A( x₁ , y₁) ≡ ( -2 , 1)  

point C( x₂ , y₂) ≡ (5 , -2)  

To Find:

d(AC) = ?

Solution:

By Applying the Pythagorean Theorem to find the distance between points A and C we get

$l(AC) = \sqrt{((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} )}$

Substituting A( x₁ , y₁) ≡ ( -2 , 1) and C( x₂ , y₂) ≡ (5 , -2) we get

$l(AC) = \sqrt{((5-{(-2}))^{2}+(-2-1)^{2} )}\\\\l(AC) = \sqrt{(5+2)^{2}+(-3)^{2}}\\\\l(AC) = \sqrt{(49+9)}\\\\l(AC) = \sqrt{58}\\\\OR\\l(AC)^{2} = 58\ units$

So the correct option is C )  58 units.

If we require Distance then l(AC) = √58 = 7.615 units