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Standard XII

Mathematics

Two Point Form of a Line

As shown in f...

Question

As shown in figure $A B C D$ is a square of side $10$ units. $E$ and $F$ are the mid points of $C D$ and $A D$ respectively. $B E$ and $F C$ intersect at $G$ . Find the length of $A G$ .

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Solution

Lets put the rectangle in a Cartesian Coordinate with $A (0, 0), B (10, 0), C (10, 10), D (0, 10)$
So, $E \equiv (5, 10)$ and $F \equiv (0, 5)$
Equation of Line $C F : y = \frac{1}{2} x + 5$
Equation of Line $E B : y = 20 - 2 x$

From Solving both equations, $G \equiv (6, 8)$
ie, Length of $A G = \sqrt{6^{2} + 8^{2}} = 10$

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As shown in figure ABCD is a square of side 10 units. E and F are the mid points of CD and AD respectively. BE and FC intersect at G. Find the length of AG.

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As shown in figure $A B C D$ is a square of side $10$ units. $E$ and $F$ are the mid points of $C D$ and $A D$ respectively. $B E$ and $F C$ intersect at $G$ . Find the length of $A G$ .