Point A lies on the line segment P Q joining P ( 6 , - 6 ) and Q ( - 4 , - 1 ) in such a way that P A P Q = 2 5 . If the point A also lies on the line 3 x + k y + 1 = 0 , find the value of k .

Suppose the coordinates of A be x , y . Here, P A P Q = 2 5 . So, P A + A Q = P Q ⇒ P A + A Q = 5 P A 2 ∵ P A = 2 5 P Q ⇒ A Q = 5 P A 2 - P A ⇒ A Q P A = 3 2 ⇒ P A A Q = 2 3 Suppose, ( x , y ) be the coordinates of A , which dives P Q in the ratio 2 : 3 internally. Then using section formula, we get, x = 2 × - 4 + 3 × 6 2 + 3 = - 8 + 18 5 = 10 5 = 2 y = 2 × - 1 + 3 × - 6 2 + 3 = - 2 - 18 5 = - 20 5 = - 4 Now, the point 2 , - 4 lies on the line 3 x + k ( y + 1 ) = 0 . Therefore, 3 × 2 + k - 4 + 1 = 0 ⇒ 3 k = 6 ⇒ k = 6 3 = 2 Therefore, k = 2 .

E M B I B E

Mathematics Textbook of Competency Based Questions for Class X>Chapter 7 - Coordinate Geometry>Exercise>Q 25

MEDIUM

10th CBSE

IMPORTANT

Earn 100

Raaji and Gagan are finding a treasure that is exactly on the straight line joining them. Raaji's location is at $(- 6, - 5)$ and Gagan's location is at $(10, 11)$ . The distance from the treasure to Raaji's location is three times that of the distance to Gagan's location.Find the coordinates of the location of the treasure.

Important Questions on Coordinate Geometry

MEDIUM

10th CBSE

IMPORTANT

Mathematics Textbook of Competency Based Questions for Class X>Chapter 7 - Coordinate Geometry>Exercise>Q 2

Point

A

lies on the line segment

P Q

joining

P (6, - 6)

and

Q (- 4, - 1)

in such a way that

\frac{P A}{P Q} = \frac{2}{5}

. If the point

A

also lies on the line

3 x + k (y + 1) = 0

, find the value of

k

.

HARD

10th CBSE

IMPORTANT

Mathematics Textbook of Competency Based Questions for Class X>Chapter 7 - Coordinate Geometry>Exercise>Q 6

If

(2, 0), (4, 4) and (6, 2)

are the vertices of the triangle

A B C

, then find the lengths of its medians.

HARD

10th CBSE

IMPORTANT

Mathematics Textbook of Competency Based Questions for Class X>Chapter 7 - Coordinate Geometry>Exercise>Q 17

Domlur and RajaRajeshwari Nagar are two suburbs in Bengaluru. The GPS coordinates of Domlur is $(12.96 ° N, 77.64 ° E)$ and that of RjaRajeshwari Nagar is $(12.92 ° N, 77.52 ° E)$ The distance between $1 °$ longitudes is $95 km$ and the distance between by $1 °$ latitude is $110 km .$

What is the shortest distance between the two locations?

HARD

10th CBSE

IMPORTANT

Mathematics Textbook of Competency Based Questions for Class X>Chapter 7 - Coordinate Geometry>Exercise>Q 19

If $A (2, 2)$ , $B (- 4, 4)$ and $C (5, - 8)$ are the vertices of a triangle, then the length of the median through vertex $C$ is

HARD

10th CBSE

IMPORTANT

Mathematics Textbook of Competency Based Questions for Class X>Chapter 7 - Pair of Linear Equations in Two Variables>Exercise>Q 71

A plumber has fixed fee which he charges once he is hired for the service. He also charges an hourly fee for his work. For $3$ hours work, he charged $₹ 1, 150$ and for $5$ hours work he charged $₹ 1, 750$ .

The hourly rate charged by the plumber is $₹$ _____.

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