Algebra help? (picture below) please show good details?

Question

Answer 1

The coordinates of A=(1,4); B=(2,5)

=>

AB=sqr[(2-1)^2+(5-4)^2]=sqr(2)

Answer 2

Distance between A(1, 4) and B(2, 5):

sqrt(2) ≈ 1.41421

Answer 3

The two-point A(1,4) and B(2,5)

the distance equation AB=sqrt{(2-1)^2+(5-4)^2}=sqrt(1+1)=sqrt 2

Answer 4

This is the same thing as your question from 4 hours ago, only using different numbers.

The distance equation between two points, derived from the Pythagorean Theorem is:

d = √[(x₁ - x₂)² + (y₁ - y₂)²]

This is an equation you will be expected to memorize.

Using the points (1, 4) and (2, 5), substitute and solve for d:

d = √[(1 - 2)² + (4 - 5)²]

d = √[(-1)² + (-1)²]

d = √(1 + 1)

d = √2

Normally I would leave it like this but since you are asked to round to 2DP, using a calculator to get a decimal approximation gives me:

d = 1.41 units

Answer 5

A (1 ; 4)   B (2 ; 5)

Distance AB

xAB = xB - xA = 2 - 1 = 1

yAB = yB - yA = 5 - 4 = 1

AB² = xAB² + yAB²

AB² = (1)² + (1)²

AB² = 2

AB = √2