Access Answers for SAT Maths Chapter 7- Coordinate geometry
Exercise7.1
1. Find the distance between the following pairs of points:
(i) (2, 3), (4, 1)
(ii) (-5, 7), (-1, 3)
(iii) (a, b), (- a, – b)
Solution:
Distance formula to find the distance between two points (x1, y1) and (x2, y2) is, say d,
2. Find the distance between the points (0, 0) and (36, 15). Can you now find the distance between
the two towns A and B discussed in Section 7.2.
Solution:
Let us consider, town A at point (0, 0). Therefore, town B will be at point (36, 15).
Distance between points (0, 0) and (36, 15)
In section 7.2, A is (4, 0) and B is (6, 0)
AB2 = (6 – 4)2 – (0 – 0)2 = 4
The distance between town A and B will be 39 km. The distance between the two towns A and B
discussed in Section 7.2 is 4 km.
3. Determine if the points (1, 5), (2, 3) and (-2, -11) are collinear.
Solution: The sum of the lengths of any two line segments is equal to the length of the third line
segment then all three points are collinear.
Consider, A = (1, 5) B = (2, 3) and C = (-2, -11)
Find the distance between points; say AB, BC and CA
,Since AB + BC ≠ CA
Therefore, the points (1, 5), (2, 3), and ( – 2, – 11) are not collinear.
4. Check whether (5, – 2), (6, 4) and (7, – 2) are the vertices of an isosceles triangle.
Solution:
Since two sides of any isosceles triangle are equal. To check whether given points are vertices of an
isosceles triangle, we will find the distance between all the points.
Let the points (5, – 2), (6, 4), and (7, – 2) are representing the vertices A, B, and C respectively.
This implies, whether given points are vertices of an isosceles triangle.
5. In a classroom, 4 friends are seated at the points A, B, C and D as shown in Fig. 7.8. Champa and
Chameli walk into the class and after observing for a few minutes Champa asks Chameli, “Don’t
you think ABCD is a square?” Chameli disagrees. Using distance formula, find which of them is
correct.
Solution:
From figure, the coordinates of points A, B, C and D are (3, 4), (6, 7), (9, 4) and (6,1).
, Find distance between points using distance formula, we get
All sides are of equal length. Therefore, ABCD is a square and hence, Champa was correct.
6. Name the type of quadrilateral formed, if any, by the following points, and give reasons for your
answer:
(i) (- 1, – 2), (1, 0), (- 1, 2), (- 3, 0)
(ii) (- 3, 5), (3, 1), (0, 3), (- 1, – 4)
(iii) (4, 5), (7, 6), (4, 3), (1, 2)
Solution:
(i) Let the points (- 1, – 2), (1, 0), ( – 1, 2), and ( – 3, 0) be representing the vertices A, B, C, and D of
the given quadrilateral respectively.
Side length = AB = BC = CD = DA = 2√2
Diagonal Measure = AC = BD = 4
Exercise7.1
1. Find the distance between the following pairs of points:
(i) (2, 3), (4, 1)
(ii) (-5, 7), (-1, 3)
(iii) (a, b), (- a, – b)
Solution:
Distance formula to find the distance between two points (x1, y1) and (x2, y2) is, say d,
2. Find the distance between the points (0, 0) and (36, 15). Can you now find the distance between
the two towns A and B discussed in Section 7.2.
Solution:
Let us consider, town A at point (0, 0). Therefore, town B will be at point (36, 15).
Distance between points (0, 0) and (36, 15)
In section 7.2, A is (4, 0) and B is (6, 0)
AB2 = (6 – 4)2 – (0 – 0)2 = 4
The distance between town A and B will be 39 km. The distance between the two towns A and B
discussed in Section 7.2 is 4 km.
3. Determine if the points (1, 5), (2, 3) and (-2, -11) are collinear.
Solution: The sum of the lengths of any two line segments is equal to the length of the third line
segment then all three points are collinear.
Consider, A = (1, 5) B = (2, 3) and C = (-2, -11)
Find the distance between points; say AB, BC and CA
,Since AB + BC ≠ CA
Therefore, the points (1, 5), (2, 3), and ( – 2, – 11) are not collinear.
4. Check whether (5, – 2), (6, 4) and (7, – 2) are the vertices of an isosceles triangle.
Solution:
Since two sides of any isosceles triangle are equal. To check whether given points are vertices of an
isosceles triangle, we will find the distance between all the points.
Let the points (5, – 2), (6, 4), and (7, – 2) are representing the vertices A, B, and C respectively.
This implies, whether given points are vertices of an isosceles triangle.
5. In a classroom, 4 friends are seated at the points A, B, C and D as shown in Fig. 7.8. Champa and
Chameli walk into the class and after observing for a few minutes Champa asks Chameli, “Don’t
you think ABCD is a square?” Chameli disagrees. Using distance formula, find which of them is
correct.
Solution:
From figure, the coordinates of points A, B, C and D are (3, 4), (6, 7), (9, 4) and (6,1).
, Find distance between points using distance formula, we get
All sides are of equal length. Therefore, ABCD is a square and hence, Champa was correct.
6. Name the type of quadrilateral formed, if any, by the following points, and give reasons for your
answer:
(i) (- 1, – 2), (1, 0), (- 1, 2), (- 3, 0)
(ii) (- 3, 5), (3, 1), (0, 3), (- 1, – 4)
(iii) (4, 5), (7, 6), (4, 3), (1, 2)
Solution:
(i) Let the points (- 1, – 2), (1, 0), ( – 1, 2), and ( – 3, 0) be representing the vertices A, B, C, and D of
the given quadrilateral respectively.
Side length = AB = BC = CD = DA = 2√2
Diagonal Measure = AC = BD = 4
