Class 10 Practice – Level 3 – Set 2 – Coordinate Geometry

Total questions: 15

The Class X students of aÂ secondary school in KrishinagarÂ have been allotted a rectangularÂ plot of land for their gardeningÂ activity. Sapling of Gulmoharare planted on the boundary at a distance of 1 m from each other. There is a triangularÂ grassy lawn in the plot asÂ shown in the Fig. TheÂ students are to sow seeds ofÂ flowering plants on the Â remaining area of the plot.

Topic: Area of a Triangle

(i) Taking $A$ as origin, find the coordinates of the vertices of the triangle.
(ii) What will be the coordinates of the vertices of $A^Δ PQR$ Â if $C$ is the origin?
Also calculate the areas of the triangles in these cases. What do you observe?

Triangle coordinates

$\displaystyle \dfrac{9}{2}$ sq. unit

$\displaystyle \dfrac{-9}{2}$ sq. unit

$\displaystyle \dfrac{6}{2}$ sq. unit

None of these

None

Find the area of ΔABC whose vertices are A(−5,7),B(−4,−5) and C(4,5).

Topic: Area of a Triangle

80 sq. units

5 sq. units

3 sq. units

20 sq. units

None

Find the area of ΔABC whose vertices are A(1,2),B(−2,3) and C(−3,−4).

Topic: Area of a Triangle

10 sq. unit

20 sq. unit

8 sq. unit

4 sq. unit

None

For what value of k(k>0) is the area of the triangle with vertices (−2,5),(k,−4) and (2k+1,10) equal to 53 square units?

Topic: Area of a Triangle

None

If P(x,y) is equidistant from the points A(7,1) and B(3,5), find the relation between x and y.

Topic: Equidistant Points

None

In what ratio does the point C(4,5) divide the join of A(2,3) and B(7,8)?

Topic: Internal Division of a Line Segment

2 : 3

4 : 6

-2 : -3

All of these

None

Find the point on x-axis which is equidistant from points A(−1,0) and B(5,0).

Topic: Equidistant Points

(8, 0)

(2, 0)

(4, 0)

None of these

None

Points A(−1,y) and B(5,7) lie on a circle with centre O(2,−3y). Find the values of y.

Topic: Circle and Distance Formula

9 or -1

7 or -1

8 or -1

None of these

None

If the centroid of ΔABC having vertices A(a,b),B(b,c) and C(c,a) is the origin, then find the values of (a + b + c).

Topic: Centroid of Triangle

None

10.

If the points A(4,3) and B(x,5) lie on the circle with centre O(2,3), then what is the value of x?.

Topic: Circle and Coordinates

None

11.

ABCD is a rectangle whose three vertices are B(4,0),C(4,3) and D(0,3). then the length of one of its diagonal is:

Topic: Distance Formula

None

12.

Find the coordinates of the point which divides the line segment joining the points (4,−3) and (8,5) in the ratio 3:1 internally.

Topic: Internal Division of a Line Segment

(7,3)

(4,3)

(8,8)

(7,8)

None

13.

Find a relation between x and y such that the point (x,y) is equidistant from the points (7,1) and (3,5).

Topic: Equidistant Points

x - z = 2 is perpendicular bisector of c.

z - y = 8 is perpendicular bisector of AD.

x - y = 4 is perpendicular bisector of AB.

x - y = 2 is perpendicular bisector of AB.

None

14.

If A(5, 2),B(2, −2) and C(−2, t) are the vertices of a right-angled triangle with ∠B = 90°, then what is the value of t?

Topic: Right-Angle Triangle

-2

None

15.

What is the value of y if the point P(–4, y) divide the line segment in a given ratio and join the points A(–6, 10) and B(3, –8) that lies on AB?

Topic: Section Formula

None

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Class 10 Practice – Level 3 – Set 2 – Coordinate Geometry

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