Points P and Q are in the line segment ab and on the same side of its midpoint- P divide ab in the ratio 3- 4 and Q divides AB in the ratio 3- 4- If PQ -2 cm-then find the length of the line segment AB-

Hi Friend , P amp;Q are closer to A since ratios are 2:3 and 3:4. AP/AB=2/5. AQ/AB=3/7. PQ=(3/7 2/5) AB = 1/35 AB. Since PQ=2, therefore, AB = 2 * 35 = 70 ...

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Standard VIII

Mathematics

Ratio in Which Centroid Divides Median

Points P and ...

Question

Points P and Q are in the line segment AB and on the same side of its midpoint. P divides AB in the ratio 2:3 and Q divides AB in the ratio 3:4. If $P Q = 2 c m,$ then find the length of the line segment AB.

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Solution

AB is the line segment which is divided by the two points P and Q in the ratios 2:3 and 3:4 respectively.
P & Q are closer to A since ratios are $2 : 3$ and $3 : 4.$
$\frac{A P}{A B} = \frac{2}{5}$
$\frac{A Q}{A B} = \frac{3}{7}$
$P Q = A Q - A P = (\frac{3}{7} - \frac{2}{5}) A B = \frac{1}{35} A B$
Since $P Q = 2 c m,$ therefore, $A B = 2 \times 35 = 70 c m$ .

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Points A and B are both in the line segment PQ and on the same side of its midpoint. A divides PQ in the ratio 2:3, and B divides PQ in the ratio 3:4. If AB=2, then the length of PQ is?

Question 1
Two line segments AB and AC include an angle of $60^{\circ}$ , where AB = 5 cm and AC = 7 cm. Locate points P and Q on AB and AC, respectively such that $A P = \frac{3}{4} A B$ and $A Q = \frac{1}{4} A C$ .Join P and Q measure the length PQ.
Thinking Process
(i) Firstly we find the ratio of AB in which P divides, it with the help of the relation $A P = \frac{3}{4} A B$
(ii) Secondly, we find the ratio of AC in which Q divides. It with the help of the relation $A Q = \frac{1}{4} A C$ .
(iii) Now, construct the line segment AB and AC in which P and Q respectively divide it in the ratio from step (i) and (ii) respectively.
(iv) Finally get the point P and Q. After that join PQ and get the required measurement of PQ.

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Points P and Q are in the line segment AB and on the same side of its midpoint. P divides AB in the ratio 2:3 and Q divides AB in the ratio 3:4. If PQ=2 cm, then find the length of the line segment AB.

AB is the line segment which is divided by the two points P and Q in the ratios 2:3 and 3:4 respectively.P & Q are closer to A since ratios are 2:3 and 3:4. APAB=25AQAB=37 PQ=AQ−AP=(37−25)AB=135AB Since PQ=2 cm, therefore, AB=2×35=70 cm.

Points P and Q are in the line segment AB and on the same side of its midpoint. P divides AB in the ratio 2:3 and Q divides AB in the ratio 3:4. If $P Q = 2 c m,$ then find the length of the line segment AB.