Advertisements
Advertisements
Question
Draw a line segment AB of length 10 cm and divide it internally in the ratio of 2:5 Justify the division of line segment AB.
Advertisements
Solution
Steps of construction:
- Draw a line segment AB of length 10 cm.
- Draw a line AX making an acute angle with AB.
- Mark 7 points A1, A2, A3, ...... A7 along AX such that AA1 = A1A2 = A1A3 = ...... = A6A7.
- Join point B with point A7.
- Through the point A2, draw a line parallel to A7B by making an angle equal to ∠AA7B at A2. This line meets AB at a point P.
As a result, point P is necessary to divide line AB internally in the ratio of 2 : 5.
Justification: In ΔAA7B, A2P || A7B.
As a result of the basic proportionality theorem,
`(A A_2)/(A_2A_7) = (AP)/(PB)` .......(i)
By the above construction,
`(A A_2)/(A_2A_7) = 2/5` ......(ii)
By equations (i) and (ii),
`(AP)/(PB) = 2/5`
Thus, AP : PB = 2 : 5
As a result, P splits the line AB in the ratio 2 : 5.
APPEARS IN
RELATED QUESTIONS
Draw a triangle ABC with BC = 7 cm, ∠B = 45° and ∠A = 105°. Then construct a triangle whose sides are`4/5` times the corresponding sides of ΔABC.
Construct a triangle ABC with BC = 7 cm, ∠B = 60° and AB = 6 cm. Construct another triangle whose sides are `3/4` times the corresponding sides of ∆ABC.
Construct an isosceles triangle with base 8 cm and altitude 4 cm. Construct another triangle whose sides are `2/3` times the corresponding sides of the isosceles triangle.
Draw a right triangle in which the sides (other than the hypotenuse) are of lengths 4 cm and 3 cm. Now construct another triangle whose sides are `3/5` times the corresponding sides of the given triangle.
Divide a line segment of length 14 cm internally in the ratio 2 : 5. Also, justify your construction.
Construct a triangle similar to a given ΔABC such that each of its sides is (2/3)rd of the corresponding sides of ΔABC. It is given that BC = 6 cm, ∠B = 50° and ∠C = 60°.
Draw a ΔABC in which BC = 6 cm, AB = 4 cm and AC = 5 cm. Draw a triangle similar to ΔABC with its sides equal to (3/4)th of the corresponding sides of ΔABC.
Draw a right triangle ABC in which AC = AB = 4.5 cm and ∠A = 90°. Draw a triangle similar to ΔABC with its sides equal to (5/4)th of the corresponding sides of ΔABC.
Construct a ΔABC in which AB = 5 cm. ∠B = 60° altitude CD = 3cm. Construct a ΔAQR similar to ΔABC such that side ΔAQR is 1.5 times that of the corresponding sides of ΔACB.
Draw a line segment AB of length 7 cm. Using ruler and compasses, find a point P on AB such that `(AP)/(AB) = 3/5 `.
Draw a ∆ABC in which AB = 4 cm, BC = 5 cm and AC = 6 cm. Then construct another triangle whose sides are\[\frac{3}{5}\] of the corresponding sides of ∆ABC ?
Construct a right triangle in which the sides, (other than the hypotenuse) are of length 6 cm and 8 cm. Then construct another triangle, whose sides are `3/5` times the corresponding sides of the given triangle.
∆AMT ~ ∆AHE. In ∆AMT, AM = 6.3 cm, ∠TAM = 50°, AT = 5.6 cm, `(AM)/(AH) = 7/5`. Construct ∆AHE.
Find the ratio in which point T(–1, 6)divides the line segment joining the points P(–3, 10) and Q(6, –8).
The line segment AB is divided into five congruent parts at P, Q, R and S such that A–P–Q–R–S–B. If point Q(12, 14) and S(4, 18) are given find the coordinates of A, P, R, B.
Draw a line segment AB of length 7 cm. Using ruler and compasses, find a point P on AB such that `(AP)/(AB)=3/5`.
Find the ratio in which the segment joining the points (1, –3) and (4, 5) is divided by the x-axis? Also, find the coordinates of this point on the x-axis.
Points P and Q trisect the line segment joining the points A(−2, 0) and B(0, 8) such that P is near to A. Find the coordinates of points P and Q.
In the figure ΔABC ~ ΔADE then the ratio of their corresponding sides is ______.
Draw seg AB of length 9 cm and divide it in the ratio 3 : 2.
ΔRHP ~ ΔNED, In ΔNED, NE = 7 cm. ∠D = 30°, ∠N = 20°, `(HP)/(ED) = 4/5`, then construct ΔRHP and ∆NED.
ΔABC ~ ΔPBR, BC = 8 cm, AC = 10 cm, ∠B = 90°, `(BC)/(BR) = 5/4` then construct ∆ABC and ΔPBR.
To divide a line segment AB in the ratio p : q (p, q are positive integers), draw a ray AX so that ∠BAX is an acute angle and then mark points on ray AX at equal distances such that the minimum number of these points is ______.
To divide a line segment AB in the ratio 5 : 7, first a ray AX is drawn so that ∠BAX is an acute angle and then at equal distances points are marked on the ray AX such that the minimum number of these points is ______.
If the perpendicular distance between AP is given, which vertices of the similar triangle would you find first?
If you need to construct a triangle with point P as one of its vertices, which is the angle that you need to construct a side of the triangle?
Match the following based on the construction of similar triangles, if scale factor `(m/n)` is.
| Column I | Column II | ||
| i | >1 | a) | The similar triangle is smaller than the original triangle. |
| ii | <1 | b) | The two triangles are congruent triangles. |
| iii | =1 | c) | The similar triangle is larger than the original triangle. |
The point W divides the line XY in the ratio m : n. Then, the ratio of lengths of the line segments XY : WX is ______.
The basic principle used in dividing a line segment is ______.
Draw a line segment of length 7 cm. Find a point P on it which divides it in the ratio 3:5.
Draw a line segment of length 7.5 cm and divide it in the ratio 1:3.
Draw a line segment AB of length 6 cm and mark a point X on it such that AX = `4/5` AB. [Use a scale and compass]
