Easy
What is a line segment ?
part of a line that has two endpoints
Points A(–7, 3), P(5, –3), B and M are on a straight line. Given P divides line segment AB in the ratio 3 : 1 and M is the midpoint of AB.
Find the coordinates of B
Point P divides the line segment joining points A and B below in the given ratios. Find the coordinates of point P.
A(7, –3), B(–3, 2) in the ratio 3AP : 2PB.
P(3,-1)
If the point R(6, 3) divides the line segment from P(4, 5) to Q(x, y) in the ratio 2 : 5, find the coordinates of Q
Q(11,-2)
Point C(1, 4) divides the straight line joining points A(–3, 6) and B(h, k) in the ratio 2 : 3.
Find the value of h and k.
h=7 , k=1
Point P(k, 2) divides the straight line joining the points A(−2, 1) and B(2, 5) in the ratio m : n.
Find the value of k
-1
Points A(–7, 3), P(5, –3), B and M are on a straight line. Given P divides line segment AB in the ratio 3 : 1 and M is the midpoint of AB.
Find the coordinates of M
M(1,-1)
Point R( p, t) divides the line segment joining points A(2h, h) and B(2p, 3t) in the ratio 2 : 3.
Express p in terms of t.
If the point R(6, 3) divides the line segment from P(4, 5) to Q(x, y) in the ratio 2 : 5, find the coordinates of the midpoint of PQ.
(15/2,3/2)
Points A(4r, r), B(e, f) and C(3e, 4f) are on a straight line. B divides the straight line AC in the ratio 3 : 4. Express e in terms of f.
e=10f
Extends infinitely
Find the ratio AP : PB such that point P(–1, 2) divides the line segment joining point A(–2, 1) and point B(2, 5).
AP:PB is 1:3
A straight line passes through points A(−2, −5) and B(6, 7). Point C divides the line segment AB in the ratio 3 : 1 while D divides AB in the ratio 1 : 1.
Find the coordinates of C
C(4,4)
A spider is at position E(–7, –5) on a graph paper and moves towards point G(13, 5) along a straight line with uniform velocity. The spider is at point P after moving for 18 seconds and arrives at point G in 1 minute. Determine the coordinates of point P
P(-1,-2)
Point P(k, 2) divides the straight line joining the points A(−2, 1) and B(2, 5) in the ratio m : n.
Find the ratio m : n
1:3
State two real life applications of coordinate geometry
Depends on students answer
Point P divides the line segment joining points A and B below in the given ratios. Find the coordinates of point P
A(3, 7), B(–7, 2) in the ratio 3 : 2.
P(-3,4)
A straight line passes through points A(−2, −5) and B(6, 7). Point C divides the line segment AB in the ratio 3 : 1 while D divides AB in the ratio 1 : 1.
Find the coordinates of D.
D(2,1)
Point P divides the line segment joining the points A and B in the ratio AP : PB. Find the ratio AP : PB and the value of k for A(1, 2), B(k, 6) and P(3, 4)
1:1 , k=5
Point P divides the line segment joining the points A and B in the ratio AP : PB. Find the ratio AP : PB and the value of k for A(–3, –2), B(2, 8) and P(–1, k)
2:3 , k=2
What is the formula for divisor of a line segment on a Cartesian plane
P(x,y)=(nx1+mx2/m+n,ny1+my2/m+n)
Point P divides the line segment joining points A and B below in the given ratios. Find the coordinates of point P.
A(– 4, –1), B(2, 5) in the ratio 2AP : PB.
P(-2,1)
Point P divides the line segment joining the points A and B in the ratio AP : PB. Find the ratio AP : PB and the value of k for A(1, k), B(–5, 10) and P(–1, 2)
1:2 , k=-2
Point P divides the line segment joining the points A and B in the ratio AP : PB. Find the ratio AP : PB and the value of k for A(k, 3), B(2, 8) and P(6, 4)
1:4 , k=7
A straight line passes through P(2, 8) and Q(7, 3). Point R divides line segment PQ such that PR = 4QR. Find the coordinates of point R.
R(6,4)