Download App

Co-Ordinate Geometry — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsCo-Ordinate Geometry3 Marks
Question
The line segment joining the points A(3, -4) and B(1, 2) is trisected at the points P(p, -2) and $\text{Q}\Big(\frac{5}{3},\text{q}\Big).$ Find the values of p and q.
✓

Answer

Point P divides the join of A(3, -4) and B(1, 2) in the ratio 1 : 2
Coordinates of P are:
$\Big(\frac{1\times1+2\times3}{1+2},\frac{1\times2+2\times(-4)}{1+2}\Big)$ or $\Big(\frac{7}{3},\frac{-6}{3}\Big)$ or $(\frac{7}{3}, -2)$
Also the point P is (p, -2) ⇒ $\text{P}=\frac{7}{3}$
Further Q is the midpoint of PB when
$\text{P}\Big(\frac{7}{3},-2\Big)$ and B(1, 2)
$\therefore$ coordinates of Q are $\bigg(\frac{\frac{7}{3}+1}{2},\frac{-2+2}{2}\bigg)$ or $\Big(\frac{5}{3},0\Big)$
Also, Q is $\Big(\frac{5}{3},\text{q}\Big)\Rightarrow\text{q}=0$
Hence, $\text{p}=\frac{7}{3}$ and q = 0

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from Co-Ordinate Geometry→Co-Ordinate Geometry — all question types→Maths STD 10 question papers→Maharashtra Board STD 10 question papers→Maharashtra Board question paper generator→

Similar questions

Water running in a cylindrical pipe of inneer diameter $7\ cm$, is collected in a container at the rate of $192.5$ litres per minute. Find the rate o flow of water in the pipe in km/hr.
→
A cone, a hemisphere and a cylinder stand on equal bases and have the same height. Show that their volumes are in the ratio 1 : 2 : 3.
→
Draw an ogive by less than method for the following data:
No. of rooms
1
2
3
4
5
6
7
8
9
10
No. of houses
4
9
22
28
24
12
78
6
5
2
→
Places A and B are 30 km apart and they are on a straight road. Hamid travels from A to B on bike. At the same time Joseph starts from B on bike, travels towards A. They meet each other after 20 minutes. If Joseph would have started from B at the same time but in the opposite direction (instead of towards A) Hamid would have caught him after 3 hours. Find the speed of Hamid and Joseph.
→
If three points $(x_1, y_1), (x_2, y_2), (x_3, y_3)$ lie on the same line, prove that $\frac{\text{y}_2-\text{y}_3}{\text{x}_2\text{x}_3}+\frac{\text{y}_3-\text{y}_1}{\text{x}_3\text{x}_1}+\frac{\text{y}_1-\text{y}_2}{\text{x}_1\text{x}_2}=0.$
→
A hemisphere of lead of radius $7\ cm$ is cast into a right circular cone of height $49\ cm$. Find the radius of the base.
→
If $\alpha$ and $\beta$ are the zeroes of the quadratic polynomial $p(s) = 3s^2 - 6s + 4$, find the value of $\frac{\alpha}{\beta}+\frac{\beta}{\alpha}+2\Big(\frac{1}{\alpha}+\frac{1}{\beta}\Big)+3\alpha\beta.$
→
Prove : $\frac{\tan A+\sec A-1}{\tan A-\sec A+1}=\frac{1+\sin A}{\cos A}$
→
Solve the following quadratic equation:$4x^2 + 4bx - (a^2 - b^2) = 0$
→
Find the least number which when divided by 20, 25, 35 and 40 leaves remainders 14, 19, 29 and 34 respectively.
→