Hope Hancock

2022-09-05

In the figure below, what are the values of $x$ and $y$?

Now, y cooridinate will be $b-k$. But how to calculate the $x$ coordinate?

Now, y cooridinate will be $b-k$. But how to calculate the $x$ coordinate?

Branson Perkins

Beginner2022-09-06Added 7 answers

The line segment seems through $(x,y)$ seems to be parallel to the $x$-axis. If you use similar triangles, you can find out the required length.

Let $(0,b)$ be point $B$, origin be $0$ and $(a,0)$ be point $A,(x,y)$ be $X$ and $(0,b-k)$ be $K$. So $K$ is similar to $\Delta BOA$. Hence,

$\frac{BK}{BO}=\frac{KX}{OA}$

$\frac{k}{b}=\frac{x}{a}$

$x=\frac{ak}{b}$

Let $(0,b)$ be point $B$, origin be $0$ and $(a,0)$ be point $A,(x,y)$ be $X$ and $(0,b-k)$ be $K$. So $K$ is similar to $\Delta BOA$. Hence,

$\frac{BK}{BO}=\frac{KX}{OA}$

$\frac{k}{b}=\frac{x}{a}$

$x=\frac{ak}{b}$

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