Vertices of Plane Figures

Q.

A right triangle is formed by connecting the 3 coordinates A, B and C as shown in figure. Find the coordinates of point B if AB and BC are parallel to the coordinate axes.

1. (5, 4)

2. (2, 1)

3. (1, 1)

4. (3, 2)

Q.

Calculate the distance between A (7, 3) and B on the -axis whose abscissa is 11.

1. 3 units

2. 5 units

3. 4 units

4. 8 units

5. 10 units

Q.

Distance of a point P(x, y) from x-axis is

1. x

2. x+y

3. xy

4. y

Q.

Points $A(-3,-7)$, $B(0,2)$ and $C(2,8)$ form the vertices of a triangle.

1. False

2. True

Q. If the vertices of a triangle are A(-a, b), B(-a, c) and C(a, c), then the area of triangle = sq units.

1. b(a-c)
2. a(c-b)
3. c(b-a)

Q.

A right triangle is formed by connecting the 3 coordinates A, B and C. Then the area of the $\Delta ABC$, if AB and BC are parallel to the coordinate axes as shown in the figure is

1. 12 sq.units

2. 10 sq.units

3. 4 sq.units

4. 6 sq.units

Q.

The points A(0, 6), B(-5, 3) and C(3, 1) are the vertices of a triangle which is _______.

1. isosceles

2. equilateral

3. scalene

4. right angled

Q.

Distance of a point Q(x, y) from y-axis is

1. xy

2. x+y

3. y

4. x

Q.

Find the area of the figure:

1. 24

2. 25

3. 26

4. 27

Q. The points (5, - 2), (6, 4) and (7, - 2) are the vertices of an ________ triangle.

1. isosceles
2. equilateral
3. scalene

Q. Two coordinates are enough to represent a point in 2 dimensional space.

1. True
2. False

Q. The vertices of a $\Delta ABC$ are $A(4,6),B(1,5)$and $C(7,2)$. A line is drawn to intersect sides $AB$ and $AC$ at $D$ and $E$ respectively, such that $\frac{AD}{AB}=\frac{AE}{AC}=\frac{1}{4}$. Calculate the area of the $\Delta ADE$ and compare it with the area of $\Delta ABC$.

Q. The triangle formed by the normal to the curve $f\left(x\right)=x^2-ax+2a$ at the point $(2,4)$ and the coordinate axes lies in second quadrant, if its area is $2$ sq units, then $a$ can be

1. $2$
2. $\frac{17}{4}$
3. $5$
4. $\frac{19}{4}$

Q.

The distance between the points (a + b, b + c) and (a – b, c – b) is _________ .

1. $2\sqrt{a^2+b^2}$

2. $2\sqrt{b^2+c^2}$

3. $2\sqrt{2}b$

4. $2\sqrt{a^2-c^2}$

Q. Is the line through $(-2,3)$ and $(4,1)$ perpendicular to the line $3x=y+1$ ?
Does the line $3x=y+1$ bisect the join of $(-2,3)$ and $(4,1)$.

Q.

If the points $A(4,3)$ and $B(x,5)$ are on the circle with the centre $O(2,3)$, find the value of $x$.

Q. A right triangle is formed by connecting the 3 coordinates A, B and C. Find the area of the $\Delta ABC$, if AB and BC are parallel to the coordinate axes as shown in the figure.
[2 Marks]