Advertisements
Advertisements
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)
Solution
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).
APPEARS IN
RELATED QUESTIONS
If the points A(k + 1, 2k), B(3k, 2k + 3) and C(5k − 1, 5k) are collinear, then find the value of k
Which point on the x-axis is equidistant from (5, 9) and (−4, 6)?
Find a point on the x-axis which is equidistant from the points (7, 6) and (−3, 4).
Show that the points A(5, 6), B(1, 5), C(2, 1) and D(6,2) are the vertices of a square.
Find the ratio in which the line segment joining (-2, -3) and (5, 6) is divided by y-axis. Also, find the coordinates of the point of division in each case.
Show that the points A (1, 0), B (5, 3), C (2, 7) and D (−2, 4) are the vertices of a parallelogram.
Determine the ratio in which the point P (m, 6) divides the join of A(-4, 3) and B(2, 8). Also, find the value of m.
If (2, p) is the midpoint of the line segment joining the points A(6, -5) and B(-2,11) find the value of p.
In what ratio is the line segment joining the points A(-2, -3) and B(3,7) divided by the yaxis? Also, find the coordinates of the point of division.
The abscissa of a point is positive in the
The points \[A \left( x_1 , y_1 \right) , B\left( x_2 , y_2 \right) , C\left( x_3 , y_3 \right)\] are the vertices of ΔABC .
(i) The median from A meets BC at D . Find the coordinates of the point D.
(ii) Find the coordinates of the point P on AD such that AP : PD = 2 : 1.
(iii) Find the points of coordinates Q and R on medians BE and CF respectively such thatBQ : QE = 2 : 1 and CR : RF = 2 : 1.
(iv) What are the coordinates of the centropid of the triangle ABC ?
Write the coordinates of the point dividing line segment joining points (2, 3) and (3, 4) internally in the ratio 1 : 5.
The coordinates of the point on X-axis which are equidistant from the points (−3, 4) and (2, 5) are
If the centroid of the triangle formed by the points (a, b), (b, c) and (c, a) is at the origin, then a3 + b3 + c3 =
The coordinates of the fourth vertex of the rectangle formed by the points (0, 0), (2, 0), (0, 3) are
The ratio in which the line segment joining points A (a1, b1) and B (a2, b2) is divided by y-axis is
What is the nature of the line which includes the points (-5, 5), (6, 5), (-3, 5), (0, 5)?
Find the point on the y-axis which is equidistant from the points (S, - 2) and (- 3, 2).
Point (3, 0) lies in the first quadrant.
The distance of the point (–4, 3) from y-axis is ______.
