Long Questions: Coordinate Geometry

# Class 8 Maths Chapter 7 Question Answers - Coordinate Geometry

Q1: The x-coordinate of a point P is twice its y-coordinate. If P is equidistant from Q (2, -5) and R(-3, 6), find the coordinates of P.
Ans:

Let the point P be (2k, k), Q(2,-5), R(-3, 6)
PQ = PR …Given
PQ2 = PR2 …[Squaring both sides
(2k – 2)2 + (k + 5)2 = (2k + 3)2 + (k – 6)2 …Given
4k2 + 4 – 8k + k2 + 10k + 25 = 4k2 + 9 + 12k + k2 – 12k + 36
⇒ 2k + 29 = 45
⇒ 2k = 45 – 29
⇒ 2k = 16
⇒ k = 8
Hence coordinates of point P are (16, 8).

Q2: Find the area of a parallelogram ABCD if three of its vertices are A(2, 4), B(2 + √3, 5) and C(2, 6).
Ans:

Since diagonal of a ||gm divides it into two equal areas.
Area of ABCD (||gm) = 2(Area of ∆ABC)
= 23 sq. units

Q3: Find the coordinates of a point P, which lies on the line segment joining the points A(-2, -2) and B(2, -4) such that AP = 3/7AB.
Ans:

Q4: If P(2, 4) is equidistant from Q(7, 0) and R(x, 9), find the values of x. Also find the distance P.
Ans:

PQ = PR …[Given]
PQ2 = PR2 … [Squaring both sides
∴ (7 – 2)2 + (0 – 4)2 = (x – 2)2 + (9 – 4)2
⇒ 25 + 16 = (x – 2)2 + 25
⇒ 16 = (x – 2)2
⇒ ±4 = x – 2 …[Taking sq. root of both sides
⇒ 2 ± 4 = x
⇒ x = 2 + 4 = 6 or x = 2 – 4 = -2

Q5: Find the value of k, if the points P(5, 4), Q(7, k) and R(9, – 2) are collinear.
Ans:

Given points are P(5, 4), Q(7, k) and R(9, -2).
x1 (y2 – y3) + x2(y3 – y1) + x3(y1 – y2) = 0 …[∵ Points are collinear
∴ 5 (k + 2) + 7 (- 2 – 4) + 9 (4 – k) = 0
5k + 10 – 14 – 28 + 36 – 9k = 0
4 = 4k
∴ k = 1

Q6: If the points A(1, -2), B(2, 3), C(-3, 2) and D(-4, -3) are the vertices of parallelogram ABCD, then taking AB as the base, find the height of this parallelogram.
Ans:

Q7: The three vertices of a parallelogram ABCD are A(3, 4), B(-1, -3) and C(-6, 2). Find the coordinates of vertex D and find the area of ABCD.
Ans:

Q8: If (3, 3), (6, y), (x, 7) and (5, 6) are the vertices of a parallelogram taken in order, find the values of x and y.
Ans:
Let A (3, 3), B (6, y), C (x, 7) and D (5, 6).

Q9: Find the ratio in which the point P(x, 2) divides the line segment joining the points A(12, 5) and B(4, -3). Also, find the value of x.
Ans:

Q10: Point P(x, 4) lies on the line segment joining the points A(-5, 8) and B(4, -10). Find the ratio in which point P divides the line segment AB. Also find the value of x.
Ans:

The document Class 8 Maths Chapter 7 Question Answers - Coordinate Geometry is a part of the Class 10 Course Mathematics (Maths) Class 10.
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## FAQs on Class 8 Maths Chapter 7 Question Answers - Coordinate Geometry

 1. What is coordinate geometry?
Ans. Coordinate geometry is a branch of mathematics that deals with the study of geometry using the principles of algebra. It involves the use of coordinate systems, such as the Cartesian coordinate system, to represent and analyze geometric shapes and their properties.
 2. How is the distance between two points calculated in coordinate geometry?
Ans. The distance between two points in coordinate geometry can be calculated using the distance formula. The formula is derived from the Pythagorean theorem and states that the distance between two points (x1, y1) and (x2, y2) is given by √((x2 - x1)² + (y2 - y1)²).
 3. What is the slope of a line in coordinate geometry?
Ans. The slope of a line in coordinate geometry is a measure of how steep the line is. It is calculated as the ratio of the vertical change (change in y-coordinates) to the horizontal change (change in x-coordinates) between any two points on the line. The formula for calculating slope is (y2 - y1)/(x2 - x1).
 4. How do you find the equation of a line in coordinate geometry?
Ans. The equation of a line in coordinate geometry can be determined using the slope-intercept form, which is y = mx + b. Here, m represents the slope of the line, and b represents the y-intercept (the point where the line crosses the y-axis). The slope can be calculated using the formula (y2 - y1)/(x2 - x1), and the y-intercept can be obtained by substituting the coordinates of any point on the line into the equation.
 5. What is the midpoint formula in coordinate geometry?
Ans. The midpoint formula in coordinate geometry is used to calculate the coordinates of the midpoint between two given points. It states that the midpoint between two points (x1, y1) and (x2, y2) is given by ((x1 + x2)/2, (y1 + y2)/2). By finding the midpoint, we can determine the point that lies exactly halfway between the two given points.

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