The points A,B and C have coordinates (0,5),(b,7) and (-4,9),respectively.If AB=BC,find the value of b.

Answer 1

Hi Sarah,

It's almost always a good idea to draw a sketch, or in this case a graph.

We're given both coordinates for points A and C, but only the y-coordinate for point B.

We need to understand that if AB = BC then B is equidistant to A and C.

There are an infinite number of points that are equidistant to A & C, but only one with a y-coordinate of 7.

Notice that if you draw a line from A to C, it crosses the horizontal line y = 7 about halfway between the points.

Do you see it yet?

This question is suddenly very easy.

Point B is the midpoint between A & C.

Do you recall the midpoint formula?

An easy way to remember it is: (Average of the x's, Average of the y's)

The average of 0 and -4 is -2.

Therefore, Point B is located at (-2, 7)

I hope this helps.

Answer 2

b² + 4 = (b + 4)² + 4; b² = b² + 8b + 16; 8b = - 16; b = - 2.