SOLUTION: Hi! I was studying analytic geometry and im having a hard to thsee queastions I dont know where to begin, I just need patterns. Hope you could help me. 1. finf the length of the

Question 957774: Hi! I was studying analytic geometry and im having a hard to thsee queastions I dont know where to begin, I just need patterns. Hope you could help me.
1. finf the length of the one leg of an isosceles triangle with vertices A(5,3),B(4,-3),and C(-1,2).
2.Find the area of a triangle whose verticea are (2,3), (6,9), (2,1).
lastly: From the distance from the line 5x=12y+26 to the point P(3,-5).
Thank you
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!

Use the distance formula,

.
.
.

From the graph, you can tell that the base of the triangle is,

and the height of the triangle is

So,

.
.
.
You can find the shortest distance by finding a perpendicular line going through (3,-5).

Perpendicular line have slopes that are negative reciprocals.

Find the point of intersection between the two lines.
Then find the distance between the intersection point and (3,-5).

So then,

So then the distance is,

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.
.

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