Given Pq Hi Find The Length Of Gh

Ever played with a compass in school? You know, that little tool that helps you draw perfect circles. Well, today we're going to chat about something similar, but in the world of math. We're talking about finding the length of a line segment, given just a few clues. Sounds like a puzzle, right?

Meet P, Q, H, and G

Imagine you're in a vast, empty field. You've got four points: P, Q, H, and G. You know the distance between P and Q (let's call it PQ), and the distance from H to G (HG). You also know the distance from P to H (PH) and from Q to G (QG).

Now, here's the kicker: you want to find the length of GH. But here's the thing, GH isn't directly given. It's like trying to find the length of a secret treasure chest buried in the field, but you only have maps to other treasures nearby.

Why is this cool?

This little math puzzle is actually a real thing in geometry, called the Pythagorean Theorem. You might have heard of it. It's like the superhero of math problems, saving the day in all sorts of shapes and sizes. But here's the fun part: we're going to use it to find our treasure, GH.

Let's Draw Some Lines

First, let's draw a line from P to G. This line, PG, is the sum of PQ and QG. So, PG = PQ + QG. Now, let's do the same from H to G. HG is the sum of PH and HG. So, HG = PH + HG.

Now, here's where the magic happens. If we subtract the second equation from the first, we get:

The figure below shows concentric circles. In the figure, OH = (1)/(2

PG - HG = (PQ + QG) - (PH + HG)

Simplifying that, we get:

PQ - PH = QG - HG

Find the length of GH, given the graph with points G(-9, -4) and H(-2, -6..

Now, look at that! The left side of the equation is the same as the right side. This means that PQ is equal to QG, and PH is equal to HG. This is like finding out that two of your friends have the same shoe size!

And the Treasure is...