1. The vertices of triangle ABC are A(7, 9), B(-3, -1) and...

1. The vertices of triangle ABC are A(7, 9), B(-3, -1) and C(5, -5) as shown in the diagram. The broken line represents the perpendicular bisector of BC. (a) Show that the equation of the perpendicular bisector of BC is y = 2x - 5. (b) Find the equation of the median from C. (c) Find the coordinates of the point of intersection of the perpendicular bisector of BC and the median from C.

Transcript

00:01 It says the vertices of triangle abc are 7, 9, negative 3, negative 1, and 5, negative 5.

00:08 The broken line represents the perpendicular bisector of bc.

00:14 We'd like to show that the equation of the perpendicular bisector of bc is y equals 2x minus 5.

00:24 Well, first things first, we want to look at the coordinates of b and c, which are negative 3, negative 1, and then we have 5 and negative 5.

00:40 So we have the slope of bc or m of bc, negative 1 to negative 5 is down 4.

00:51 From negative 3 to positive 5 is 8, which means the slope of this line is negative 1 half.

01:01 So the slope of a line perpendicular to bc is going to have to be a positive 2, which we have here.

01:13 Keep in mind, as we look at the slope of this line, we now need to figure out this point.

01:23 If this is indeed the perpendicular bisector, we know the midpoint of these two is going to be halfway between negative 3 and 5 is going to be 1.

01:39 Halfway between negative 1 and negative 5 is going to be negative 3.

01:48 So we could take the 2 is our slope, we have an x coordinate of 1 and a y value of negative 3.

01:56 And we could solve for b coincidentally enough, we do get b is negative 5.

02:03 So we do wind up with the equation y equals 2x minus 5.

02:08 So let's find the equation of the median from c.

02:14 Well, using that same mentality, we know the point a is 7, 9...

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