Which two points of concurrency always remain inside the triangle, and why?

1 answer:

4 0

The point of concurrency is the point where three or more lines, segments, or rays intersect forming a point. Out of the four namely the Centroid, Incenter, Circumcenter, and Orthocenter, only the Centroid and Incenter is always located inside the triangle.

Centroid: where the medians intersect

Incenter: where the angle bisectors intersect

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PQ is rotated 180 degrees clockwise about P. What are the coordinates of P' and Q'?

Salsk061 [2.6K]

The co ordinates of P' is (-7,-2) and Q' is (-16, -8)

Explanation

PQ is rotated 180 degrees clockwise about P. It means P and P' are the same points.

According to the graph, the coordinates of P is (-7, -2) and Q is (2, 4)

When PQ is rotated 180 degrees clockwise about P, then P or P' will be the mid-point of Q and Q'

Suppose, the co ordinate of Q' is (x, y)

Now according to the mid-point formula, the coordinate of P or P' will be: $(\frac{x+2}{2},\frac{y+4}{2})$ , which is actually at (-7, -2)