Question
Download Solution PDFIf centroid of triangle with vertices (4, p), (-1, -1) and (3, 5) is given by the mid-point of (1, 4) & (q, 2), then p2 + q2 will be:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Vertices of triangle are (4, p), (-1, -1) and (3, 5)
Concept:
Centroid of a Triangle: The point where the three medians of the triangle intersect.
Let’s consider a triangle. If the three vertices of the triangle are A(x1, y1), B(x2, y2), C(x3, y3).
The centroid of a triangle =
Mid-point: If two points are (x1, y1) and (x2, y2), then mid point is given by
Calculation:
We know that, centroid of triangle is given by
G =
Therefore, for given triangle, we will get centroid
G =
According to question, G is the mid-point of (1, 4) & (q, 2). Therefore, by using mid-point formula
On comparing both side
⇒ q = 3 & q = 5
⇒ p2 + q2 = 34
Hence, option 4 is correct.
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