Advertisements
Advertisements
Question
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`.
Solution
It is given that`(AP)/(AB)=3/5`.
`therefore (AP)/(PB)=(AP)/(AB-AP)=3/(5-3)=3/2`
Thus, point P divides line segment AB in the ratio 3: 2.
To draw a line segment AB of length 7 cm and mark a point P (using ruler and compass) such that `(AP)/(PB)=3/5 i,e, (AP)/(PB)=3/2`, the following steps are to be followed:
Step 1: Draw line segment AB of length 7 cm and draw a ray AX making an acute angle with line segment AB.
Step 2: Locate 5 (2 + 3) points i.e., A1, A2, A3, A4 and A5 on AX such that AA1 = A1 A2 = A2 A3 and so on.
Step 3: Join BA5.
Step 4: Through point A3 , draw a line parallel to BA5 (by making an angle equal to ∠AA5 B) at A3 intersecting AB at point P.
Now, P is the required point on line segment AB of length 7 cm. This point satisfies the condition`(AP)/(AB)=3/5`.
APPEARS IN
RELATED QUESTIONS
Draw a line segment of length 7.6 cm and divide it in the ratio 5:8. Measure the two parts. Give the justification of the construction.
Construct a triangle similar to a given ΔABC such that each of its sides is (5/7)th of the corresponding sides of Δ ABC. It is given that AB = 5 cm, BC = 7 cm and ∠ABC = 50°.
Draw a triangle ABC with side BC = 6 cm, ∠C = 30° and ∠A = 105°. Then construct another triangle whose sides are `2/3` times the corresponding sides of ΔABC.
∆ABC ~ ∆LBN. In ∆ABC, AB = 5.1 cm, ∠B = 40°, BC = 4.8 cm, \[\frac{AC}{LN} = \frac{4}{7}\]. Construct ∆ABC and ∆LBN.
Find the ratio in which point T(–1, 6)divides the line segment joining the points P(–3, 10) and Q(6, –8).
Given A(4, –3), B(8, 5). Find the coordinates of the point that divides segment AB in the ratio 3 : 1.
ΔPQR ~ ΔABC. In ΔPQR, PQ = 3.6cm, QR = 4 cm, PR = 4.2 cm. Ratio of the corresponding sides of triangle is 3 : 4, then construct ΔPQR and ΔABC
To construct a triangle similar to a given ΔABC with its sides `3/7` of the corresponding sides of ΔABC, first draw a ray BX such that ∠CBX is an acute angle and X lies on the opposite side of A with respect to BC. Then locate points B1, B2, B3, ... on BX at equal distances and next step is to join ______.
The image of construction of A’C’B a similar triangle of ΔACB is given below. Then choose the correct option.
The basic principle used in dividing a line segment is ______.
