In math worksheet on line-segment joining the points, we will solve different types of questions.
Recall the formula for the distance between two given points (x₁, y₁) and (x₂, y₂) is
√{(x₂ - x₁)² + (y₂ - y₁)²}
To know more about the distance between the two or more co-ordinate points and the different types of examples Click Here.
Follow the above formula to solve the below questions given in the worksheet on line-segment joining the points.
1. Find the distance between each of the following pair of points:
(i) (5, 10) and (- 3, 4)
(ii) (- 13, -11) and (-2, - 9)
(iii) ( 2 + √3, 2 - √3) and (- 2 + √3, 2 + √3)
(iv) (x,- y) and ( - x,y)
(v) (a cos θ, a sin θ) and (a cos φ, a sin φ)
(vi) (a + b, c - d) and (a - b, c + d)
(vii) (x + 2, 0) and (0, x - 2)
(viii) (at₁², 2at₁) and (at₂², 2at₁).
2 (i) fir If the distance between the points (x, - 7) and (3, - 3) be 5, find x.
(ii) The distance between the points (7, 3) and (2, y) is √41; find the ordinate of the second point.
(iii) If the distance between the points (p, - 5) and (2, p) be 13 units, find the value of p.
(iv) The square of the distance between the points (- 2, a) and (a, - 3) is 85 find a.
3. (i) Show that the points (2, 2), (- 2, - 2) and (-2√3, 2√3) are the vertices of an equilateral triangle.
(ii) 'Prove that the points (- 1, 5), (3, 2) and (- 1, - 1) are the vertices of an isosceles triangle. Find the co-ordinates of its centroid.
(iii) Show that the points (5, 6), (1, 2) and ( 9, 2) are the vertices of a right-angled triangle ; find its area.
(iv) Prove that the points (7, 9), (3, - 7) and (- 3, 3) form a right-angled isosceles triangle.
4. ABC is an equilateral triangle ; the co-ordinates of the vertices B and C are (2a, 6a) and (2a + √3a, 5a) respectively. Find the co-ordinate of the vertex A.
5. (i) find the point on the x-axis which is equidistant from the points
(2, -1)and(- 3, 4).
(ii) Find the condition so that the point (a, b) may be equidistant from the points (8, 4) and (- 2, - 4).
(iii) If the point (x, y) be equidistant from the points (10, 0), (0, - 10) and (- 8, 6) then prove that x = 0, y = 0.
(iv) Find the co-ordinates of the point which is equidistant from the points (-2, 3), (2, 1) and(5, 3).
6. (1) The co-ordinates of the vertices of a triangle are (0, 0), (5, 3) and (3, 5) respectively ; find the circum-centre and circum-radius of the triangle.
(ii) the co-ordinates of the circum-centre of the triangle ARC are (8, 3) ; if the "co intimates of the vertices A, B and C be (x, -9 ), (y, - 2) and (- 5, 3) respectively , find the values of x and y.
Answers for the worksheet on line-segment joining the points are given below to check the exact answers of the above questions.
1. (i) 10
(ii) 5√5
(iii) 2√7
(iv) 2√(x² + y²)
(v) 2a |sin (θ - φ)/2|
(vi) 2√(b² + d²)
(vii) √[2(x² + 4)]
(viii) a |t₁ - t₂|√(t₁ – t₁)² + 4) units.
2. (i) 6 or, 0
(ii) 7 or, (- 1)
(iii) 7 or (- 10)
(iv) -9 or, 4
3. (ii) (1/3, 2)
(iii) 16 sq. units
4. ( 2a, 4a ) or, ( 2a + √3a, 7a)
5. (i) (- 2, 0)
(ii) 5a + 4b = 15
(iv) (3/2, 5)
6. (i) (17/8, 17/8) and (17√2)/8 units.
(ii) x = 13 or 3 and y = 20 or (-4).
● Co-ordinate Geometry
11 and 12 Grade Math
From Worksheet on Line-Segment Joining the Points to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Dec 03, 24 01:29 AM
Dec 03, 24 01:19 AM
Dec 02, 24 01:47 PM
Dec 02, 24 01:26 PM
Nov 29, 24 01:26 AM
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.