Question

Ryan, from a very young age, was fascinated by the twinkling of stars and the vastness of space. He always dreamt of becoming an astronaut one day. So, he started to sketch his own rocket designs on the graph sheet. One such design is given below :

Based on the above, answer the following questions:

i. Find the mid-point of the segment joining F and G.    (1) 

ii. a. What is the distance between the points A and C?   (2)

OR

b. Find the coordinates of the points which divides the line segment joining the points A and B in the ratio 1 : 3 internally.    (2)

iii. What are the coordinates of the point D?    (1)

Answer 1

i.  F (-3, 0) = (x₁, y₁), G (1, 4) = (x₂, y₂)

Midpoint Formula - `((x_1 + x_2)/2, (y_1 + y_2)/2)`

= `((x_1 + x_2)/2, (y_1 + y_2)/2)`

= `((- 3 + 1)/2, (0 + 4)/2)`

= `(- 2/2, 4/2)`

= (-1, 2)

The midpoint of the segment joining F and G is (-1, 2)

ii. (a)  A = (3, 4) = (x₁, y₁), C = (-1, -2) = (x₂, y₂)

Distance Formula - `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)`

= `sqrt((-1 - 3)^2 + (-2 - 4)^2)`

= `sqrt((- 4)^2 + (-6)^2)`

= `sqrt(16 + 36)`

= `sqrt52`

= 7.21 (approx.)

OR

(b) A = (3, 4) = (x₁, y₁), B = (3, 2) = (x₂, y₂)

∴ Let the ration be m : n = 1 : 3

Section Formula = `((mx_2 + nx_1)/(m + n), (my_2 + ny_1)/(m + n))`

= `((1(3) + 3(3))/(1 + 3), (1(2) + 3(4))/(1 + 3))`

= `((3 + 9)/4, (2 + 12)/4)`

= `(12/4, 14/4)`

= `(3, 14/4)`

iii. The Coordinates of the point D is (-2, -5).