A ladder is resting on the side of a house - use the coordinates to find the length of the ladder

[@stevendebettencourt7651]

Length of the ladder? No problemo. Because we are given the endpoints of the ladder in coordinate form, the best way to go about this is to draw two legs of a right triangle with the ladder length as its hypotenuse. Then we can use the Pythagorean Theorem to solve for the ladder length. Let’s define the third point of said triangle. The first two points are the endpoints of the ladder, given as (4,2) and (10,5). The third point is the point below (10,5) and to the right of (4,2) which will for our right triangle, which turns out to be the point (10,2). Now, we need the lengths of the two legs of our right triangle. These should be easy to figure out as they lie along the lines x=10 and y=2. The base leg is 10-4=6 units long, while the height leg is 5-2=3 units high. Now, we call upon the Pythagorean Theorem to save us: x^2 + y^2 = z^2 6^2 + 3^2 = z^2 36 + 9 = z^2 z^2 = 45 |z| = sqrt(45) z = +- sqrt(9*5) z = +- 3*sqrt(5) We throw out the negative value as nonsensical, since distances must be at least 0. So, the ladder is 3*sqrt(5) units long. Using 2.24 as an approximate value for sqrt(5), we get about 6.72 units. Any questions?

[@chrisdissanayake6979]

Answer: The length of the ladder is 3 √5 units ----------- In the right angled triangle, the length of the ladder represents the diagonal. Let it be X units. The other sides are 10-4=6 units and 5-2=3 units According to Pythagorean theorem, X^2 = 6^2 + 3^2 X^2 = 36 + 9 = 45 X= √45 = √9 * √5 X = 3 √5 units

[@Poult100]

Ah, ha! I see the relationship between the distance formula and Pythagoras' theorem. And then you mentioned it at the end! 😊

[@tomtke7351]

(4,2) to (10,5) a^2+b^2=c^2 (10-4)^2+(5-2)^2=L^2 6^2+3^2=L^2 36+9=L^2 45=L^2

[@hazevthewolf178]

I guess that in your universe, objects float above the ground! The answer (the square root of 45) is obvious, if one knows the theorem of Pythagoras.

[@raya.pawley3563]

Thank you

[@panlomito]

(10-4)² + (5-2)² = L² so L = V(36+9) = V45 = 3V5 ( ~ 6.71 L³)

[@adgf1x]

3(5^0.5) unit .length

[@russelllomando8460]

sr 45 or 3 sr 5 base is 6 (10 - 4) height is 3 (5 - 2) used the pyth therom. forgot about the D formula. thanks for the fun

[@josephlaura7387]

3sq.root of5

[@lizardfirefighter110]

Holy smokes I did it all in my head ( no paper) and got “6”! I was just .7 off, C+ , or B😂😂😂

[@mrsoikawa]

Too many mathematical theories at play here.