Question

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

A. 4 units

B. 6 units

C. 7 units

D. 5 units

Answer 1

5 Units

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

D. 5 units

Explanation:

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

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

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

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

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

`\[= √(16+9)\]`

`\[= √(25)\]`

`\[= 5\]`

Hence the correct answer is D. 5 units