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Show that the triangle with A (1, 3), B (-3, 1) and C (2, -2) is an isosceles triangle. Find:
a. perimeter
b. equations of the altitude
c. the point of intersection at the altitude y=8


Sagot :

first determine the distance from point A to B, Point B to C then C to A.

using the formula for distance between two points.

[tex]d= \sqrt{( x_{2}-x_{1})^2+( y_{2}-y_{1})^2 } [/tex]

solve for distance from A to B

[tex]d= \sqrt{( -3-1)^2+( 1-3)^2 } [/tex]

[tex]d=2 \sqrt{5} [/tex]  [tex]units[/tex]

solve for distance from B to C

[tex]d= \sqrt{( 2-(-3))^2+( -2-1)^2 } [/tex]

[tex]d= \sqrt{34} [/tex]  [tex]units[/tex]

solve for distance from C to A

[tex]d= \sqrt{( 1-(2))^2+( 3-(-2))^2 } [/tex]

[tex]d= \sqrt{34} [/tex]  [tex]units[/tex]