ICSE Class X Math 2015 Paper

In the given figure $A B C$ is a triangle and $B C$ is parallel to the $y$ -axis. $A B$ and $A C$ intersects the $y$ -axis at $P$ and $Q$ respectively.

Question : 25 of 52

Marks: +1, -0

Find the length of

A B

and

A C

Solution:

Coordinates of

A(4,0)

and

B(-2,3)

\; \text{ Length of } \; A B \; = \sqrt{(-2-4)^2+(3-0)^2}

\; = \sqrt{36+9} = \sqrt{45}

\; = 3 \sqrt{5} \; \text{ units. } \;

Coordinates of

A(4,0)

and

C(-2,-4)

\; \text{ Length of } \; A C \; = \sqrt{(-2-4)^2+(-4-0)^2}

\; = \sqrt{36+16} = \sqrt{52}

\; = 2 \sqrt{13} \; \text{ units. } \;

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