The coordinates of the point P which is equidistant from the three vertices of the β³AOB as shown in the figure is
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Official Solution
Correct Option:
(1)
The point P is equidistant from the three vertices of triangle ΞOAB. This means that P is the circumcenter of ΞOAB. Since O is at the origin (0, 0), triangle ΞOAB has a right angle at O. The circumcenter of a right triangle is the midpoint of the hypotenuse. The coordinates of A are (0, 2y) and the coordinates of B are (2x, 0). The midpoint of AB is given by:
Thus, the coordinates of P are (x, y). Final Answer:
The final answer is [1]
02
PYQ 2025
medium
mathematicsID: ap-polyc
The coordinates of the point which divides the line segment joining the points and internally in the ratio are
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Official Solution
Correct Option:
(1)
Step 1: Recall the section formula. The coordinates of a point that divides the line segment joining and internally in the ratio are given by the section formula: However, the standard internal division formula with (where is the part towards and towards ) is: where and are the ratios from to and to . Step 2: Interpret the ratio . The ratio means divides such that the segment from to is parts and from to is parts. The correct formula for internal division is: But the standard form with as the ratio in which divides internally from to is: which seems reversed. The correct interpretation is: where is the part of , is the part of . Step 3: Match with options. Option (1): , This matches the standard section formula where is the ratio in which divides internally, with associated with and with . Options (2), (3), and (4) have different combinations or signs, which do not align with the internal division formula. Step 4: Verify the formula. For example, if , (ratio 1:1, midpoint): which is the midpoint, confirming option (1). Step 5: Select the correct answer. The coordinates are , matching option (1).
03
PYQ 2025
medium
mathematicsID: ap-polyc
The distance between the points and is
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Official Solution
Correct Option:
(3)
Step 1: Use the distance formula. The distance between two points and is given by: Here, the points are and , so , , , . Step 2: Compute the differences. , . Step 3: Calculate the distance. Simplify : Step 4: Correct the calculation. Recompute carefully: However, letΓ’β¬β’s verify the coordinates and options: , , , but option (3) is . Recheck distance: , Possible typo in options or points. If intended and : , which matches option (3). Step 5: Select the correct answer. Assuming a possible typo in the second point (e.g., instead of ), the distance fits option (3). With given , itΓ’β¬β’s , but answer (3) suggests correction to points.
About Distance Formula - AP-POLYCET
Distance Formula is a vital chapter for AP-POLYCET aspirants. Mastering the concepts covered in this chapter is essential for securing a top rank.
By rigorously practicing the previous year questions associated with this chapter, you can identify high-yield topics, understand the examiner's perspective, and boost your confidence during the actual exam.
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