Analysis geometry

Question

А(7; -2), В(4; -1), С(5; 2).

1. Find the equation of the median of АВС, which passes through the vertex С.

2. Find the equation of the height of triangle АВС, which passes through the vertex В. 3. Find the projection of the point А on the straight line ВС.

ІІ. М1(-1; 5; 3), М2(3; 0; 4), 5x+3y-z+2=0 (1).

3. Find the equation of the plane which passes through the point М1 and parallel to the plane (1).

4. Find the equation of the plane which passes through the point М1 and parallel to the plane (1). 5.Find the equation of the straight line which passes through the

point М2 and perpendicular to the plane (1).

Answer 1

Here's the triangle:

5-4=1

2-(-1)=3

a^2+b^2=c^2

1^2+3^2=10^.5=3.162=a

7-4=3

2-(-1)=3

3^2+3^2=18^.5=4.243=b

7-5=2

-2-2=-4

2^2+(-4)^2=20^.5=4.472=c

This is a rt triangle.

a/sinα=b/sinβ=c (sin of a rt <=1)

3.162/sinα=4.243/sinβ=4.472=c

sinα=3.162/4.472=.745; α=48.184

sinβ=4.243/4.472=.949; β=71.565

α+β+γ=180: 48.18°+71.565°-180=60.25°