he line l:x+3=0𝑙:𝑥+3=0 is the axis of symmetry of the equilateral triangle ABC𝐴𝐵𝐶. Knowing that A=(−7,−2)𝐴=(−7,−2) determine the coordinates of the vertices B𝐵 and C𝐶.
Question
he line l:x+3=0𝑙:𝑥+3=0 is the axis of symmetry of the equilateral triangle ABC𝐴𝐵𝐶. Knowing that A=(−7,−2)𝐴=(−7,−2) determine the coordinates of the vertices B𝐵 and C𝐶.
Solution
The line x+3=0 is the axis of symmetry of the equilateral triangle ABC. This means that the x-coordinate of the vertex A, which is -7, is 3 units away from the line of symmetry (since -7 + 3 = -4).
Since the line of symmetry bisects the base of the equilateral triangle, the x-coordinates of the vertices B and C will be 3 units to the left and right of the line of symmetry, respectively.
So, the x-coordinate of B will be -4 - 3 = -7 and the x-coordinate of C will be -4 + 3 = -1.
The y-coordinate of B and C will be the same as that of A, which is -2.
Therefore, the coordinates of the vertices B and C are B(-7, -2) and C(-1, -2).
Similar Questions
What are the coordinates of the image of point L (-7, 4) after the triangle is reflected over the y = x line of symmetry? Answer in (x, y) format (____, ____)
𝑁 is the point of intersection of the lines with equations 2𝑥−𝑦=−9 and 3𝑥+5𝑦=−7Write down the coordinates of 𝑁.
Find the coordinates of the vertex of the graph of the following equation: 𝑦=(𝑥−3)(𝑥−7)y=(x−3)(x−7)
Instructions: Given the vertex of a quadratic function, find the axis of symmetry.Vertex: (−1,3)
Instructions: Given the function, state the vertex.y=−3(x+7)2−6𝑦=−3(𝑥+7)2−6Vertex =(=( ,, )
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.