Prove that the points (2a, 4a), (2a, 6a) & (2a + √3a, 5a) are the vertices of an equilateral triangle.

Question

Answer

To prove that the points (2a, 4a) and (2a, 6a) lie on the same vertical line, we need to show that their x-coordinates are the same.

The x-coordinate of the point (2a, 4a) is 2a, which is also the x-coordinate of the point (2a, 6a). Therefore, both points lie on the same vertical line.

We can also represent this geometrically by drawing a graph with the x-axis representing the horizontal line and the y-axis representing the vertical line. The points (2a, 4a) and (2a, 6a) would both lie on the vertical line passing through the point (2a, 0) on the x-axis.

Answer

Distance between (2a,4a), (2a,6a) is 2a.
Likely find the distance between other points by using the distance formula in coordinate geometry

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