Question

the vertices of an isosceles triangle are (-10,1 ), B(-6, 3), and C(-4, 7)
What is the equation of the triangles line of symmetry?
y=-x-3
y=-x+3
y=x+3
y=x-3

Answer 1

Look at the picture.

$D\left(\dfrac{-10+(-4)}{2};\ \dfrac{1+7}{2}\right)\to D\left(\dfrac{-14}{2};\ \dfrac{8}{2}\right)\to D(-7;\ 4)$

$y=ax+b\\\\D(-7;\ 4);\ B(-6;\ 3)\\\\DB:\ \left\{\begin{array}{ccc}4=-7a+b\\3=-6a+b\end{array}\right\ |subtract\ both\ sides\\\\1=-a\to\ a=-1\\\\4=-7\cdot(-1)+b\\7+b=4\ \ \ |-7\\b=-3\\\\DB:y=-x-3$

Answer: y = -x - 3

Answer 2

Answer:y=-x-3

Step-by-step explanation: