Â Â Â Â Â Â (ii) Let
Â Â Â Â Â Â Â and
Â Â Â Â Â Â Area of
Â Â Â Â Â Â
Â Â Â Â Â Â
Â Â Â Â Â Â
Â Â Â Â Â Â = 32 sq. units
Q.2 Â Â In each of the following find the value of 'k' for which the points are collinear :Â
Â Â Â Â Â (i) (7, â€“2),Â (5, 1), (3, k) Â Â Â (ii) (8, 1), (k, â€“ 4), (2, â€“ 5)
Sol.Â Â Â (i) Let the given points beÂ and .Â
Â Â Â Â Â Â These points lie on a line if
Â Â Â Â Â Â Area
Â Â Â Â Â Â
Â Â Â Â Â Â
Â Â Â Â Â Â
Â Â Â Â Â Â
Â Â Â Â Â Â 2k = 8
Â Â Â Â Â Â k = 4
Â Â Â Â Â Â Hence, the given points are collinear for k = 4
Â Â Â Â Â (ii) Let the given points beÂ
Â Â Â Â Â If the given points are collinear, then
Â Â Â Â Â
Â Â Â Â Â
Â Â Â Â Â
Â Â Â Â Â Â â€“Â 6k = â€“ 18
Â Â Â Â Â k = 3
Â Â Â Â Â Hence, the given points are collinear for k = 3.
Q.3 Â Â Find the area of the triangle formed by joining the mid-points of the sides of the triangleÂ whose vertices are (0, â€“1), (2, 1), andÂ (0, 3). Find the ratio of this area to the area of the Â given triangle.
Sol.Â Â Â Let
Â Â Â Â Â Â and be the vertices of .
Â Â Â Â Â Â Area
Â Â Â Â Â Â
Â Â Â Â Â Â
Â Â Â Â Â Â Â = 1 sq. unit (numerically)Â Â Â
Â Â Â Â Â Â Area
Â Â Â Â Â =
Â Â Â Â Â
Â Â Â Â Â sq. units
Â Â Â Â Â Â Let ,i.e., (1, 2), , i.e., Â (1, 0) and , i.e., (0, 1) are the vertices
Â Â Â Â Â of Â formed by joining the mid-points of the sides of .
Â Â Â Â Â Ratio of the area to the area = 1 : 4.
Q.5 Â Â You have studied in class IX (Chapter 9 Example 3) that a median of a triangle divides it into two triangles of equal areas. Verify this result for ABC whose vertices are A(4, â€“6), B(3, â€“2) and C(5, 2).
Sol. Â Â Â Since AD is the median of , therefore, D is the mid-point of BC. Coordinates of D are
Â Â Â Â Â Â ,i.e., (4, 0).
Â Â Â Â Â Â Area ofÂ
Â Â Â Â Â Â
Â Â Â Â Â Â
Â Â Â Â Â Â = 3sq. units (numerically)
Â Â Â Â Â Â
Â Â Â Â Â Â
Â Â Â Â Â Â = 3 sq. units (numerically)
Â Â Â Â Â Â Clearly, area = area
Â Â Â Â Â Â Hence, the median of the triangle divides it into two triangles of equal areas.
Â
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Question 3 mein kaun sa formula use hua hai
Bro dono triangle ka area nikala hai and then compare kiya. 1st ka answer 1 sq.unit ka ya and 2nd ka answer 4 sq.units aaya that is why 1:4.
Formula: area of triangle
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