Class 10 Maths1)If the point P(2, 1) lies on the line segment joining points A(4, 2) and B(8, 4), then
AP = \(1 \over 2 \) AB
Class 10 Maths2)
If the area of the triangle formed by the points (x, 2x), (-2, 6) and (3, 1) is 5 square units, then x =
2
Area of triangle whose vertices are (x, 2x),(-2,6) and (3, 1)
\(=\frac{1}{2}\left[x_{1}\left(y_{2}-y_{3}\right)+x_{2}\left(y_{3}-y_{1}\right)+x_{3}\left(y_{1}-y_{2}\right)\right]\)
\(=\frac{1}{2}[x(6-1)+(-2)(1-2 x)+3(2 x-6)]\)
\(=\frac{1}{2}[5 x-2+4 x+6 x-18]\)
\(=\frac{1}{2}[15 x-20]\)
∴Area = 5 square units
\(\therefore \frac{1}{2}(15 x-20)=5 \Rightarrow 15 x-20=10\)
\(\Rightarrow 15 x=10+20=30 \Rightarrow x=\frac{30}{15}=2\)
∴ x = 2
Class 10 Maths3)
(0, 3), (4, 0) and (– 4, 0) are the vertices of
an isosceles triangle
Class 10 Maths4)
The line 2x + y - 4 = 0 divides the line segment joining A(2, -2) and B(3, 7) in the ratio
2:9
Class 10 Maths5)
The distance between the points (0, 5) and (–5, 0) is
\(5\sqrt{2}\)
Class 10 Maths6)
The points A (-4, 0), B(4, 0) and C(0, 3) are the vertices of a
isosceles triangle
Class 10 Maths7)
The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is
12
Class 10 Maths8)
If points (a, 0), (0, b) and (1, 1) are collinear, then \(\frac{1}{a} + \frac{1}{b}\) is
1
Class 10 Maths9)The mid-point of the line segment joining the points A (-2, 8) and B (- 6, - 4) is
(– 4, 2)
Class 10 Maths10)
The area of the triangle with vertices (a, b+c), (b, c+a) and (c, a+b) is
0