Question

If A = (7,9) and B = (3, 12), what is the length of AB

Answer 1

Answer:

5 Units

Step-by-step explanation:

From A(7,9) to B(3,12) you rise 4 from 3 to 7

From A(7,9) to B(3,12) you run 3 from 9 to 12

Now we have 2 sides of a triangle, we need the hypotenuse which is AB. All we have to do is insert our numbers into the Pythagorean Thereom$a^{2}+ b^{2} =c^{2} \\3^{2} +4^{2} =c^{2} \\9+16=c^{2} \\\sqrt 25=\sqrt c^{2} \\5=c$

Answer 2

Answer:

D. 5 units

Step-by-step explanation:

Coordinates of A = (7,9) = (x1,y1)

Coordinates of B = (3,12) = (x2,y2)

Length of line segment AB = $\[\sqrt{(x2-x1)^{2}+(y2-y1)^{2}}\]$

$\[= \sqrt{(3-7)^{2}+(12-9)^{2}}\]$

$\[= \sqrt{(-4)^{2}+(3)^{2}}\]$

$\[= \sqrt{16+9}\]$

$\[= \sqrt{25}\]$

$\[= 5\]$

Hence the correct answer is D. 5 units