Short Answer Questions: Coordinate Geometry - 2

Class 10 Maths Chapter 7 Question Answers - Coordinate Geometry - 2

Q12. Show that the triangle PQR formed by the points  and is an equilateral triangle.

OR

Name the type of triangle PQR formed by the points   and

Q13. The line joining the points (2, − 1) and (5, − 6) is bisected at P. If P lies on the line 2x + 4y + k = 0, find the value of k.
Sol. We have A (2, − 1) and B (5, − 6).
∵ P is the mid point of AB,
∴ Coordinates of P are:

Since P lies on the line 2x + 4y + k = 0
∴ We have:

Q14. Find the point on y-axis which is equidistant from the points (5, − 2) and (− 3, 2).
Sol. ∵ Let P is on the y-axis
∴ Coordinates of P are: (0, y)

Q15. The line joining the points (2, 1) and (5, − 8) is trisected at the points P and Q. If point P lies on the line 2x − y + k = 0, find the value of k.
Sol.

Q.16. Find the point on x-axis which is equidistant from the points (2, − 5) and (− 2, 9).
Sol. ∵ The required point ‘P’ is on x-axis.
∴ Coordinates of P are (x, 0).
∴ We have

AP = PB
⇒ AP2 = PB2
⇒ (2 − x)2 + (− 5 + 0)2 =(− 2 − x)2 + (9 − 0)2
⇒ 4 − 4x + x2 + 25 = 4 + 4x + x2 + 81
⇒ 4x + 25 = 4x + 81
⇒ − 8x = 56

∴ The required point is (−7, 0).

Q17. The line segment joining the points P (3, 3) and Q (6, − 6) is trisected at the points A and B such that A is nearer to P. It also lies on the line given by 2x + y + k = 0. Find the value of k.

Sol. ∵ PQ is trisected by A such that

Q18. Find the ratio in which the points (2, 4) divides the line segment joining the points A (− 2, 2) and B (3, 7). Also find the value of y.
Sol. Let P (2, y) divides the join of A (− 2, 2) and B (3, 7) in the ratio k:1
∴ Coordinates of P are:

Q19. Find the ratio in which the point (x, 2) divides the line segment joining the points (− 3, − 4) and (3, 5). Also find the value of x.

Sol. Let the required ratio = k : 1

∴ Coordinates of the point P are:

But the coordinates of P are (x, 2)

Q20. If P (9a – 2, –b) divides the line segment joining A (3a + 1, −3 ) and B (8a, 5) in the ratio 3 : 1, find the values of a and b.
Sol. ∵ P divides AB in the ratio 3 : 1
∴ Using the section formula, we have:

− b = 3 or b = −3
⇒ 36a − 8= 27a + 1 and b= −3
⇒ 9a = 9 and b = −3

Thus, the required value of a = 1 and b = −3

Q21. Find the ratio in which the point (x, − 1) divides the line segment joining the points (− 3, 5) and (2, − 5). Also find the value of x.
Sol. Let the required ratio is k : 1

Q22. Find the co-ordinates of the points which divide the line segment joining A(2, −3) and B(−4, −6) into three equal parts.
Sol. Let the required points are P(x1, y1) and Q(x2, y2)
∴ Using section formula, we have:

Thus, the coordinates of the required points are (0, −4) and (−2, 5)

Q23. If the mid-point of the line segment joining the point A(3, 4) and B(k, 6) is P(x, y) and x + y – 10 = 0, then find the value of k.
Sol. ∵ Mid point of the line segment joining A(3, 4) and B(k, 6)

Q24. Point P, Q, R and S divide the line segment joining the points A (1, 2) and B (6, 7) in 5 equal parts. Find the co-ordinates of the points P, Q and R.

∴  P, Q, R and S, divide AB into five      equal parts.
∴ AP = PQ = QR = RS = SB
Now, P divides AB in the ratio 1 : 4
Let, the co-ordinates of P be x and y.
∴ Using the section formula i.e.,

Next, Q divides AB in the ratio 2 : 3
∴ Co-ordinates of Q are :

Now, R divides AB in the ratio 3 : 2
⇒  Co-ordinates of R are :

The co-ordinates of P, Q  and R are respectively:(2, 3), (3, 4) and (4, 5).

The document Class 10 Maths Chapter 7 Question Answers - Coordinate Geometry - 2 is a part of the Class 10 Course Short & Long Answer Questions for Class 10.
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FAQs on Class 10 Maths Chapter 7 Question Answers - Coordinate Geometry - 2

 1. What is coordinate geometry?
Ans. Coordinate geometry is a branch of mathematics that deals with the study of geometric figures using a coordinate system. It involves the use of coordinates to represent points, lines, curves, and other geometric objects, and allows us to analyze their properties and relationships using algebraic methods.
 2. How is a point represented in coordinate geometry?
Ans. In coordinate geometry, a point is represented by an ordered pair of numbers called coordinates. The first number represents the horizontal distance from a fixed reference line called the x-axis, and the second number represents the vertical distance from another fixed reference line called the y-axis. The coordinates are written in the form (x, y).
 3. What is the equation of a straight line in coordinate geometry?
Ans. The equation of a straight line in coordinate geometry is generally written in the form y = mx + c, where m represents the slope of the line and c represents the y-intercept (the point where the line intersects the y-axis). This equation relates the x and y coordinates of any point on the line.
 4. How do you find the distance between two points in coordinate geometry?
Ans. To find the distance between two points (x1, y1) and (x2, y2) in coordinate geometry, we can use the distance formula. The distance formula is given by: sqrt((x2 - x1)^2 + (y2 - y1)^2) This formula calculates the straight-line distance between the two points by finding the square root of the sum of the squares of the differences in their x and y coordinates.
 5. How can we determine if three points are collinear in coordinate geometry?
Ans. To determine if three points (x1, y1), (x2, y2), and (x3, y3) are collinear in coordinate geometry, we can calculate the slope of the line formed by any two of the points. If the slopes of both the lines formed by (x1, y1) and (x2, y2), and (x2, y2) and (x3, y3) are equal, then the three points lie on the same line and are collinear. If the slopes are not equal, then the points are not collinear.

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