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?
y = x + 1
y = x - 1
y = x
y = -x + 1

Answer 1

Based on the calculations, the equation of the triangle's line of symmetry is equal to: B. y = x - 1.

How to determine the equation of the triangle's line of symmetry?

First of all, we would determine the midpoint where the line of symmetry passes through points A and B:

Midpoint at point A = (3 + 7)/2 = 10/2 = 5.

Midpoint at point B = (6 + 2)/2 = 8/2 = 4.

Point D = (5, 4)

Mathematically, the standard equation of a line is given by y = ax + b.

D(5, 4); 4 = 5a + b   ....equation 1.

C(4, 3); 3 = 4a + b    ....equation 2.

Subtracting eqn. 2 from eqn. 1, we have:

1 = a

Next, we would find the value of b:

4 = 5a + b

4 = 5(1) + b

b = 4 - 5

b = -1.

Therefore, the equation of the triangle's line of symmetry is given by:

y = ax + b

y = x(1) + (-1)

y = x - 1.

Read more on line of symmetry here: brainly.com/question/10152876

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