Question

I do not understand the distance formula in Algebra 1...can anyone explain it please

Answer 1

If you have two points (x1,y1) and (x2,y2) in a cartesian coordinate system (xy-axis). The line segment between them can also be connected by a line segment that follows the x-axis, and another line segment that follows the y-axis. This is a right triangle with a hypothenuse (distance from P1 to P2), vertical side (y2-y1), and a horizontal side x2-x1) .The hypothenuse is the lenght of the distance from P1 to P2, and is related to the pythagorean theorem as side c^2=a^2+b^2. side a would be the horizontal, side b the vertical. so (distance)^2= a^2 +b^2 \[d=\sqrt{(x_{2}-x _{1})^2+(y _{2}-y _{1})^2}\]. It's really just a play on the pythagorean theorem relating the two points to the sides of a right triangle.