Question 12 Marks
Find the midpoint of the line segment joining the following pair of point :
$( a+3, 5b), (3a-1, 3b +4).$
Answer
Coordinates of $R$ are,
$R(x, y)=R\left(\frac{a+3+3 a-1}{2}, \frac{5 b+3 b+4}{2}\right) $
$=R(2 a+1,4 b+2)$ View full question & answer→Question 22 Marks
Find the midpoint of the line segment joining the following pair of point :
$(3a-2b, Sa+7b)$ and $(a+4b, a-3b)$
Answer
Coordinates of $C$ are,
$C(x, y)=C\left(\frac{a+4 b+3 a-2 b}{2}, \frac{a-3 b+5 a+7 b}{2}\right) $
$=C(2 a+b, 3 a+2 b)$ View full question & answer→Question 32 Marks
Find the midpoint of the line segment joining the following pair of point :
$(a+b, b-a)$ and $(a-b, a+b)$
Answer
Coordinates of $R$ are,
$O(x, y)=O\left(\frac{a+b+a-b}{2}, \frac{b-a+a+b}{2}\right) $
$=O(a, b)$ View full question & answer→Question 42 Marks
Find the midpoint of the line segment joining the following pair of point :
$( -3, 5)$ and $(9, -9)$
Answer
Coordinates of $R$ are,
$R(x, y)=R\left(\frac{-3+9}{2}, \frac{5-9}{2}\right)$
$=R(3,-2)$ View full question & answer→Question 52 Marks
Find the midpoint of the line segment joining the following pair of point :
$(4,7)$ and $(10,15)$
Answer
Coordinates of $P$ are
$P(x, y)=P\left(\frac{4+10}{2}, \frac{7+15}{2}\right)$
$=P(7,11)$ View full question & answer→Question 62 Marks
Find the distance between the following point :
$(\sec \theta , \tan \theta)$ and $(-\tan \theta , \sec \theta)$
Answer$A(\sec \theta, \tan \theta), B(-\tan \theta, \sec \theta) $
$ A B=\sqrt{(-\tan \theta-\sec \theta)^2+(\sec \theta-\tan \theta)} $
$ =\sqrt{\tan ^2 \theta+\sec ^2 \theta+2 \tan \theta \sec \theta+\sec ^2 \theta+\tan ^2 \theta-2 \tan \theta \cdot \sec \theta} $
$=\sqrt{2 \sec ^2 \theta+2 \tan ^2 \theta} \text { units }$
View full question & answer→Question 72 Marks
Find the distance between the following point :
$(\sin \theta , \cos \theta)$ and $(\cos \theta , -\sin \theta)$
Answer$A(\sin \theta, \cos \theta), B(\cos \theta,-\sin \theta)$
$A B=\sqrt{(\cos \theta-\sin \theta)^2(-\sin \theta-\cos \theta)^2}$
$=\sqrt{\cos ^2 \theta+\sin ^2 \theta-2 \cos \theta \sin \theta+\sin ^2 \theta+\cos ^2 \theta+2 \cos \theta \sin \theta}$
$=\sqrt{2} \text { units }$
View full question & answer→Question 82 Marks
Find the distance between the following point :
$(p+q,p-q)$ and $(p-q, p-q)$
Answer$A(p+q, p-q), B(p-q, p-q) $
$ A B=\sqrt{(p-q-p)^2+(p-q-p+q)^2} $
$ =\sqrt{4 q^2+0} $
$ =2 q \text { units }$
View full question & answer→Question 92 Marks
Find the distance between the following pairs of point in the coordinate plane :
$(13 , 7)$ and $(4 , -5)$
Answer$A=(13,7), B=(4,-5) $
$ A B=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2} $
$ =\sqrt{(4-13)^2+(-5-7)^2} $
$=\sqrt{81+144} $
$ =\sqrt{225}$
$ =15 \text { units. }$
View full question & answer→Question 102 Marks
Find the distance between the following pairs of point in the coordinate plane :
$(4 , 1)$ and $(-4 , 5)$
Answer$A=(4,1), B=(-4,5) $
$ A B=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2} $
$ =\sqrt{(-4-4)^2+(5-1)^2} $
$ =\sqrt{64+16} $
$ =\sqrt{80}=4 \sqrt{5} \text { units. }$
View full question & answer→Question 112 Marks
Find the distance between the following pairs of point in the coordinate plane :
$(7 , -7)$ and $(2 , 5)$
Answer$A(7,-7), B(2,5) $
$ A B=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$
$ =\sqrt{(2-7)^2+(5+7)^2}$
$ =\sqrt{25+144}$
$ =\sqrt{169}=13 \text { units. }$
View full question & answer→Question 122 Marks
Find the distance of the following point from the origin :
$(13 , 0)$
Answer$P(0,0), Q(13,0) $
$ P Q=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$
$=\sqrt{(13-0)^2+(0-0)^2} $
$=\sqrt{169} $
$ =13 \text { units }$
View full question & answer→Question 132 Marks
Find the distance of the following point from the origin :
$(0 , 11)$
Answer$P(0,0), Q(0,11)$
$ P Q=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2} $
$ =\sqrt{(0-0)^2+(11-0)^2}$
$=\sqrt{121} $
$ =11 \text { units }$
View full question & answer→Question 142 Marks
Find the distance of the following point from the origin :
$(8 , 15)$
Answer$P=(0,0), Q=(8,15) $
$ P Q=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$
$ =\sqrt{(8-0)^2+(15-0)^2} $
$=\sqrt{64+225}$
$ =\sqrt{289} $
$=17 \text { units }$
View full question & answer→Question 152 Marks
Find the distance of the following point from the origin :
$(6 , 8)$
Answer$P=(0,0) Q=(6,8) $
$ P Q=\sqrt{(6-0)^2+(8-0)^2} $
$=\sqrt{36+64} $
$ =\sqrt{100}$
$=10 \text { units }$
View full question & answer→Question 162 Marks
Find the distance of the following point from the origin :
$(5 , 12)$
Answer$P Q=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2} $
$ =\sqrt{(12-0)^2+(5-0)^2}$
$ =\sqrt{144+25} $
$=\sqrt{169}$
$=13 \text { units. }$
View full question & answer→Question 172 Marks
Find the distance between the following pair of point in the coordinate plane.
$(1 , 3)$ and $(3 , 9)$
Answer$A=(1,3), B=(3,9)$
$ A B=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$
$ =\sqrt{(3-1)^2+(9-3)^2} $
$=\sqrt{4+36} $
$ =\sqrt{40} \text { units }=2 \sqrt{10} \text { units. }$
View full question & answer→Question 182 Marks
Find the distance between the following pair of point in the coordinate plane :
$(5 , -2)$ and $(1 , 5)$
Answer$A(5,-2), B(1,5) $
$ A B=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2} $
$ =\sqrt{(1-5)^2+(5+2)^2} $
$ =\sqrt{16+49}$
$ =\sqrt{65} \text { units. }$
View full question & answer→