Question

The vertices of an isosceles triangle are A(3, 6), B(7, 2), and C(4, 3).

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

Answer 1

BC=AC means C is the vertex so the line joining C to mid point of AB is the line of symmetry,
mid point of AB=(5,4)
equation = y-4=x-3,y-x=1.

Answer 2

cool thanks

Answer 3

sure thing

Answer 4

the answers it is giving me are
y = x + 1
y = x - 1
y = x
y = -x + 1

Answer 5

would it be Y=X+1 ??

Answer 6

@Siri15

Answer 7

actually

Answer 8

The answer is y = x-1

Answer 9

thanks again

Answer 10

If you plot the 3 given points on graph paper, then join them, it becomes apparent that the point
(4,3) is the vertex of the isosceles triangle.
The line of symmetry will therefore be the perpendicular from (4,3) to the mid-point of the base, which
is the line joining (3,6) and (7,2).
The mid-point of the base is found by averaging the x, then the y, coordinates of the line's end points.
This would be [ (7+3)/2 , (6+2)/2 ]
=(5,4)
Now all we have to do in find the equation of the line that joins the vertex (4,3) to the mid-point of
the base, (5,4)
The equation has the form y = mx+b
m = slope = (4-3) / (5-4) = 1/1 = 1
y = 1x + b
Since (4,3) lies on the line, it "satisfies" the equation of that line.
3 = 4 +b
3-4 = b
-1 = b
The equation is y = x-1
Note: If using a graph is not allowed, then yo have to calculate the distances (length) of each
side of the triangle to find 2 that are the same. Use the Distance formula.
D^2 = (x2-x1)^2 + (y2-y1)^2

Answer 11

ahh. makes sense