Question

Match the given points with the distances between them.

• A. $\sqrt{2}$ units
• B. 1 unit
• C. $\sqrt{2}6$ units
• D. $2\sqrt{1}0$ units

Answer 1

Distance between two points A$(x_1,y_1)$ and B$(x_2,y_2)$ is given as
AB =$\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$

i) A(3, 4) and B(4,5)
AB is the distance between the points A and B.
AB =$\sqrt{(4-3{)}^2+(5-4{)}^2}$ = $\sqrt{1+1}$= $\sqrt{2}$
AB = $\sqrt{2}$ units

ii) P(4,5) and Q(5,5)
PQ is the distance between the points P and Q.
PQ =$\sqrt{(5-4{)}^2+(5-5{)}^2}$ = $\sqrt{1+0}$= 1
PQ = 1 unit

iii) E(6,3) and F(7,8)
EF is the distance between the points E and F.
EF =$\sqrt{(7-6{)}^2+(8-3{)}^2}$ = $\sqrt{1+25}$= $\sqrt{26}$
EF= $\sqrt{26}$ units

iv) M(1,2) and N(3,8)
MN is the distance between the points M and N.
MN=$\sqrt{(3-1{)}^2+(8-2{)}^2}$ = $\sqrt{4+36}$= $\sqrt{4}0$
EF= $\sqrt{4}0$ = $\sqrt{4\times 10}$ = $2\sqrt{10}$ units