The vertices of an isosceles triangle are a(-10, 1), b(-6, 3) and c(-4, 7).

what is the equation of the triangle's line of symmetry?

y = -x - 3
y = -x + 3
y = x + 3
y = x - 3

Part A

y = 5x - 2 start with the second equation

7x - 8 = 5x - 2 ... replace y with 7x-8, which is from the first equation

7x-8+8 = 5x-2+8 add 8 to both sides

7x = 5x+6

7x-5x = 5x+6-5x ... subtract 5x from both sides

2x = 6

2x/2 = 6/2 divide both sides by 2

x = 3

Use x = 3 to find the value of y

y = 7x - 8

y = 7*3 - 8

y = 21 - 8

y = 13

We can use the other equation as well to get the same result for y

y = 5x - 2

y = 5*3 - 2

y = 15 - 2

y = 13

Part B

This is If you graphed both equations on the same xy coordinate grid.

This point is on both lines at the same time; therefore, the coordinate values of this point satisfy both equations at the same time. As shown below

y = 7x - 8

13 = 7*3 - 8 plug in (x,y) = (3,13)

13 = 13   true equation; this point is on the first line

repeat for the second equation

y = 5x - 2

13 = 5*3 - 2

13 = 13 ... true equation; this point is on the second line

both equations are true when (x,y) = (3,13), so this point is on both lines at the same time.