SECTION B — Very Short Answer Type Questions [2 Marks Each]
- 2 Marks Q26. If $(1, 2)$, $(4, y)$, $(x, 6)$, and $(3, 5)$ are the vertices of a parallelogram taken in order, find $x$ and $y$
- 2 Marks Q27. Find the centroid of a triangle whose vertices are $(1, 4)$, $(-2, 3)$, and $(5, -2)$.
- 2 Marks Q28. Two opposite vertices of a square are $(-1, 2)$ and $(3, 2)$. Find the coordinates of the remaining two vertices.
- 2 Marks Q29. Find the length of the median through vertex $A$ of $\triangle ABC$ whose vertices are $A(7, -3)$, $B(5, 3)$, and $C(3, -1)$.
- 2 Marks Q30. If the mid-points of the sides of a triangle are $(1, 2)$, $(0, -1)$, and $(2, -1)$, find the coordinates of its vertices.
- 2 Marks Q31. Find the ratio in which the line $2x + y - 4 = 0$ divides the line segment joining the points $(2, -2)$ and $(3, 7)$.
- 2 Marks Q32. If $P(-1, y)$ and $Q(5, 7)$ lie on a circle with center $C(2, -3)$, find the value of $y$.
- 2 Marks Q33. Find the coordinates of the point $P$ on the line segment joining $(1, 2)$ and $(6, 7)$ such that $AP = \frac{2}{5}AB$.
- 2 Marks Q34. If $A(-2, 4)$, $B(0, 0)$, and $C(4, 2)$ are the vertices of $\triangle ABC$, find the length of median $BD$
- 2 Marks Q35. Find the coordinates of the point dividing the line segment joining $(3, 5)$ and $(7, 9)$ externally in the ratio $3:1$. *(Note: standard internal section focus, or extend ratio practice)* -> Let's use internal ratio: find point dividing line segment joining $(1, 3)$ and $(2, 7)$ in ratio $3:2$.
- 2 Marks Q36. Find the area of the triangle whose vertices are $(2, 3)$, $(-1, 0)$, and $(2, -4)$.
- 2 Marks Q37. Find the area of the triangle with vertices $(5, 2)$, $(4, 7)$, and $(7, -4)$.
- 2 Marks Q38. In each of the following find the value of '$k$' for which the points are collinear: $(7, -2), (5, 1), (3, k)$.
- 2 Marks Q39. Find the value of $k$ if the points $A(2, 3)$, $B(4, k)$, and $C(6, -3)$ are collinear.
- 2 Marks Q40. Find the area of the quadrilateral whose vertices, taken in order, are $(-4, -2)$, $(-3, -5)$, $(3, -2)$, and $(2, 3)$.
- 2 Marks Q41. If $A(-5, 7)$, $B(-4, -5)$, $C(-1, -6)$, and $D(4, 5)$ are the vertices of a quadrilateral, find its area.
- 2 Marks Q42. Find the area of $\triangle ABC$ with vertices $A(1, -1)$, $B(-4, 6)$, and $C(-3, -5)$
- 2 Marks Q43. For what value of $p$ are the points $(p, 1)$, $(2, 1)$, and $(4, 5)$ collinear?
- 2 Marks Q44. Find the area of the triangle formed by the points $(0, 0)$, $(5, 0)$, and $(0, 8)$.
- 2 Marks Q45. If the points $(a, 0)$, $(0, b)$, and $(1, 1)$ are collinear, prove that $\frac{1}{a} + \frac{1}{b} = 1$.
- 2 Marks Q46. Find the area of the triangle formed by the coordinate axes and the line $2x - 3y + 12 = 0$.
- 2 Marks Q47. Show that the points $(a, b+c)$, $(b, c+a)$, and $(c, a+b)$ are collinear.
- 2 Marks Q48. Find the perimeter of the triangle formed by the points $(0, 4)$, $(0, 0)$, and $(3, 0)$
- 2 Marks Q49. If the vertices of a triangle are $(1, k)$, $(4, -3)$, and $(-9, 7)$ and its area is $15$ square units, find the values of $k$.
- 2 Marks Q50. Find the third vertex of a triangle if its two vertices are $(-1, 4)$ and $(5, 2)$ and its centroid is $(0, -3)$.
Academic Repository Disclaimer & எச்சரிக்கை அறிவிப்பு :
English: These model solutions are structured to global academic standards for self-assessment and practice purposes. Students are advised to verify with official textbooks for board examinations.
தமிழ்: இந்த மாதிரி கணிதத் தீர்வுகள் மாணவர்களின் சுய கற்றல் மற்றும் பயிற்சித் திறனுக்காக உலகளாவிய கல்வித் தரத்தில் உருவாக்கப்பட்டுள்ளன. தேர்வுகளுக்குத் தயாராகும் போது உங்கள் அதிகாரப்பூர்வ பாடப்புத்தகத்துடன் சரிபார்க்கவும்.
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