Download App

Equation of a Line — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsEquation of a Line3 Marks
Question
The following figure shows a parallelogram ABCD whose side AB is parallel to the x-axis. ∠A = 60° and vertex C = (7, 5). Find the equations of BC and CD.
Image
✓

Answer

Since, ABCD is a parallelogram,
$\angle A + \angle B = 180^\circ$
$\angle B = 180^\circ - 60^\circ = 120^\circ$
Slope of $BC =\tan 120^\circ = \tan (90^\circ + 30^\circ) = \cot 30^\circ =\sqrt{3}$
Equation of the line BC is given by:
$y − y_1 = m (x − x_1)$
$y-5=\sqrt{3}(x-7)$
$y-5=\sqrt{3} x-7 \sqrt{3}$
$y=\sqrt{3} x+5-7 \sqrt{3}$
Since, CD || AB and AB || x-axis, slope of CD = Slope of AB = 0
Equation of the line CD is given by:
$y − y_1 = m (x - x_1)$
$y − 5 = 0(x − 7)$
$y = 5$

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 sum]" from Equation of a Line→Equation of a Line — all question types→Mathematics STD 10 question papers→ICSE Board STD 10 question papers→ICSE Board question paper generator→

Similar questions

Solve the given inequation and graph the solution set on the number line :
$2 y-3 < y+1 \leq 4 y+7, y \in R$
→
Find the value of $x$, which satisfies the inequation $-2 \leq \frac{1}{2}-\frac{2 x}{3} \leq 1 \frac{5}{6}, x \in N$
Graph the solution set on the number line.
→
Puneet has a Recurring Deposit Account in the Bank of Baroda and deposits $Rs.140$ per month for $4$ years. If he gets $Rs.8,092$ on maturity, find the rate of interest given by the bank.
→
A hollow sphere of internal and external radii 6 cm and 8 cm respectively is melted and reactinto small cones of base radius 2 cm and height 8 cm. Find the number of cones.
→
Prove that $\frac{\tan ^2 \theta}{(\sec \theta-1)^2}=\frac{1+\cos \theta}{1-\cos \theta}$
→
In ABCD is a cyclic quadrilateral; O is the centre of the circle. If BOD = 160°, find the measure of BPD.
→
If $A=\left[\begin{array}{ll}2 & 3 \\ 1 & 2\end{array}\right]$ find $x$ and $y$ so that $A^2-x A+y \mid$
→
Given:
A = {x: 11x – 5 > 7x + 3, x ∈ R} and
B = {x: 18x – 9 ≥ 15 + 12x, x ∈ R}.
Find the range of set A ∩ B and represent it on the number line.
→
Suresh has joined a factory which pays wages by cheque only. He opens a S.B. account on Feb. 1, and his passbook has the following entries Upto 1st April of the year.
Date Particulars Withdrawals(₹) Deposits(₹) Balance(₹)
Feb. 1 By cash - 50·00 50·00
Feb. 2 By salary - 1,000·00 1,050·00
Feb. 4 To withdrawn slip 200·00 - 850·00
Feb. 15 By overtime allowance - 300·00 1,150·00
Feb. 24 To Aslam 100·00 - 1,050·00
March 1 By salary - 1,000·00 2,050·00
March 7 To cheque no. 212 500·00 - 1,550·00
March 21 To cheque no. 213 700·00 - 850·00
March 27 To self 400·00 - 450·00
Apr. 1 By salary - 1,000·00 1,450·00
Apr. 11 By interest - - -

He closes the account on 11th April. Complete the entries for 11th April at the rate of 5%
→
Without solving the quadratic equation $6x^2 – x – 2=0,$ find whether $x = 2/3$ is a solution of this equation or not.
→