Answer to Question #152886 in Analytic Geometry for HIRWA Rodrigue

Question

A=(4,3), B=(6,-2), C=(2,+1) Find lengths of sides in triangle ABC.

Answer 1

A=(4,3), B=(6,-2), C=(2,+1) Find lengths of sides in triangle ABC.

In order to find AB, BC, AC length of triangle ABC, there is 2 ways:

1st way is by pythagor theorem.

2nd one is the formula for finding the distance between two points.

1)

To find AB, BC, AC we need to use the Pythagorean theorem on S$_2$ , S$_3$ , S$_1$ , respectively.

AB= $\sqrt{2^2+5^2}=\sqrt{29};$

BC= $\sqrt{4^2+3^2}=\sqrt{25}=5;$

AC= $\sqrt{2^2+2^2}=\sqrt{8}=2\sqrt2;$

2)

To find AB, BC, AC we need to use formula $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

AB= $\sqrt{(6-2)^2+(-2-3)^2}=\sqrt{2^2+5^2}=\sqrt{29};$

BC= $\sqrt{(2-6)^2+(1-(-2))^2}=\sqrt{4^2+3^2}=\sqrt{25}=5;$

AC= $\sqrt{(2-4)^2+(1-3)^2}=\sqrt{2^2+2^2}=\sqrt{8}=2\sqrt2;$