Geometry question! Please help ASAp

Hi Kate,

Assuming, you want the shortest distance from the point (p) to the line that goes through the two points (-5,2) and (-2,6)...

first determine the equation of the line that goes through the 2 points.

y=(4/3)x + (26/3)... Using standard techniques for finding a line through 2 points

now determine the point on the line that is closed to the point (p). This would be the point on the line that is perpendicular to the point (p) which will have an equation with a slope of -1/(4/3) = (-3/4) and goes through the point (p). So this equation
is

y=-(3/4)x - (7/4)... again using the same technique from above given 2 points

Now the intersection of the two lines is at (-5,2), using a technique of solving two linear equations. Which happens to be one of the points of the first line that was given.

so the distance between point (p) and the closest point on the line (-5,2) is

d = (6

^{2}+8^{2})^{1/2}=10