23.
(03.03 LC)
Look at triangle ABC.
Coordinate grid shows negative 5 to positive 5 on the x axis and y axis at intervals of 1. A triangle ABC is shown with A at ordered pair 4, 5, B at ordered pair 1, 2, and C at ordered pair 4, 2.
What is the length of side AB of the triangle? (1 point)
Square root of 6
3
Square root of 18
6
AC is vertical, they have the same x
BC is horizontal, they have the same y
so just counting , AC = 3 , BC = 3
so AB^2 = 3^2 + 3^2 = 18
AB = √18 = 3√2
I see that choice
Well, it looks like we're dealing with a triangle here. And we need to find the length of the side AB. Let me put on my mathematician clown nose and crunch some numbers.
To find the length of a side of a triangle, we can use the distance formula. The distance formula is like a long-lost cousin of the Pythagorean theorem, except it doesn't care about right angles.
Using the distance formula, the length of AB is the square root of [(x2 - x1)^2 + (y2 - y1)^2].
So, let's plug in our coordinates. We have A at (4, 5) and B at (1, 2).
Plugging in those values, we get the length of AB as the square root of [(1 - 4)^2 + (2 - 5)^2].
Well, (-3)^2 is 9, and (-3)^2 is 9 too. So, we're left with the square root of 18.
Voila! The length of side AB is the square root of 18.
To find the length of side AB of the triangle, you can use the distance formula. The distance formula calculates the distance between two points in a coordinate plane.
The formula for distance between two points (x1, y1) and (x2, y2) is:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Using the given coordinates for points A (4, 5) and B (1, 2), we can substitute the values into the formula:
Distance = √((1 - 4)^2 + (2 - 5)^2)
= √((-3)^2 + (-3)^2)
= √(9 + 9)
= √18
Therefore, the length of side AB of the triangle is the square root of 18.
To find the length of side AB of the triangle, we can use the distance formula. The distance formula is derived from the Pythagorean theorem and calculates the distance between two points in a coordinate plane.
The distance formula is given by:
distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
In this case, we need to find the distance between points A(4, 5) and B(1, 2).
Let's substitute these coordinates into the distance formula:
distance = √[(1 - 4)² + (2 - 5)²]
= √[(-3)² + (-3)²]
= √[9 + 9]
= √18
Therefore, the length of side AB of the triangle is the square root of 18 or √18.