Distance formula and section formula - One Line Questions
1.
Find the coordinates of the point which divides the line segment joining (1, 5) and (4, 2) externally in the ratio 1:2. —
(-2, 7)
2.
Find the coordinates of the point which divides the line segment joining (3, -4) and (-6, 5) internally in the ratio 1:2. —
(-3, -2)
3.
Find the coordinates of the point dividing the line segment joining (-4, -2) and (2, 4) externally in the ratio 1:2. —
(-8, -10)
4.
If a point P divides the line segment joining A(x1, y1) and B(x2, y2) in the ratio k:1, then the coordinates of P are: —
((kx2 + x1)/(k+1), (ky2 + y1)/(k+1))
5.
If a point P divides the line segment joining A(x1, y1) and B(x2, y2) externally in the ratio m:n, what are the coordinates of P? —
((mx2 - nx1)/(m-n), (my2 - ny1)/(m-n))
6.
If a point P divides the line segment joining A(x1, y1) and B(x2, y2) internally in the ratio m:n, what are the coordinates of P? —
((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n))
7.
What is the section formula for internal division? —
((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n))
8.
What are the coordinates of the centroid of a triangle with vertices (x1, y1), (x2, y2), and (x3, y3)? —
((x1+x2+x3)/3, (y1+y2+y3)/3)
9.
Find the coordinates of the point which divides the line segment joining A(-1, 7) and B(4, -3) internally in the ratio 2:3. —
(1, 3)
10.
Find the coordinates of the point which divides the line segment joining A(5, -2) and B(-1, 4) externally in the ratio 3:2. —
(13, -10)
11.
Find the point which divides the line segment joining (2, -5) and (4, 5) in the ratio 3:2 internally. —
(14/5, 1)
12.
Find the coordinates of the point which divides the line segment joining (1, 2) and (3, 4) in the ratio 1:1. —
(2, 3)
13.
Find the coordinates of the point which divides the line segment joining A(2, 1) and B(5, 7) in the ratio 1:2. —
(11/3, 5/3)
14.
A point P divides the line segment joining A(1, 2) and B(6, 7) in the ratio 2:3. Find the coordinates of P. —
(3, 4)
15.
Find the coordinates of the point which divides the line segment joining A(5, 9) and B(1, -3) internally in the ratio 1:3. —
(4, 6)
16.
Find the coordinates of the midpoint of the line segment joining A(3, 4) and B(7, 8). —
(5, 6)
17.
Find the coordinates of the point which divides the line segment joining (1, 2) and (2, 3) in the ratio 1:2. —
(5/3, 8/3)
18.
Find the coordinates of the point which divides the line segment joining (1, -3) and (4, 5) externally in the ratio 2:1. —
(7, 13)
19.
Find the coordinates of the point which divides the line segment joining (2, 3) and (5, 6) externally in the ratio 2:1. —
(8, 9)
20.
If the point (x, y) divides the line joining (x1, y1) and (x2, y2) in the ratio k:1, then x = ? —
(kx2 + x1)/(k+1)
21.
If a point P divides the line segment joining A(x1, y1) and B(x2, y2) internally in the ratio m:n, then the y-coordinate of P is: —
(my2 + ny1)/(m+n)
22.
Find the ratio in which the point P(x, y) divides the line segment joining A(x1, y1) and B(x2, y2). —
(x2-x)/(x-x1) : (y2-y)/(y-y1)
23.
If the points (0, 0), (a, b), and (c, d) form a triangle, its area is: —
1/2 |ad - bc|
24.
What is the area of the triangle formed by the points (0, 0), (x1, y1), and (x2, y2)? —
1/2 |x1*y2 - x2*y1|
25.
What is the perimeter of the triangle with vertices A(0, 0), B(3, 0), and C(0, 4)? —
12
26.
Find the distance between the parallel lines 3x + 4y - 5 = 0 and 6x + 8y + 10 = 0. —
15/sqrt(5)
27.
If the distance between (a, 2) and (3, 4) is 2, what is the value of 'a'? —
3 or -3
28.
If a point P divides the line segment joining A(x1, y1) and B(x2, y2) such that AP = 3PB, then P divides AB internally in the ratio: —
3:1
29.
In what ratio does the point P(2, 3) divide the line segment joining A(-2, 4) and B(3, -7)? —
4:5
30.
What is the distance between the points (2, 3) and (5, 7)? —
5
31.
If the points (1, 1), (2, 3), and (3, k) are collinear, find the value of k. —
5
32.
What is the distance between the points (-2, 3) and (-2, 8)? —
5
33.
Find the value of k if the distance between (k, -1) and (3, 2) is 5. —
7 or -1
34.
If point P divides AB externally in the ratio m:n (m > n), then the distance AP is what fraction of the total distance AB? —
m/(m-n)
35.
If point P divides the line segment AB internally in the ratio m:n, then the distance AP is what fraction of the total distance AB? —
m/(m+n)
36.
If a point P divides AB internally in ratio m:n, and externally in ratio p:q, then: —
m*q = n*p
37.
The section formula is a generalization of which formula? —
Midpoint formula
38.
If the origin divides the line segment joining A(x1, y1) and B(x2, y2) in the ratio m:n, then: —
mx2 + nx1 = 0 and my2 + ny1 = 0
39.
The distance formula is derived from which theorem? —
Pythagorean theorem
40.
What is the distance between the points (x, y) and (-x, -y)? —
2*sqrt(x^2 + y^2)
41.
What is the distance between two points (x1, y1) and (x2, y2) in a Cartesian plane? —
sqrt((x2 - x1)^2 + (y2 - y1)^2)
42.
What is the distance of the point (6, -2) from the origin (0, 0)? —
sqrt(40)
43.
What is the distance between the points (a+b, a-b) and (a-b, a+b)? —
2*sqrt(2)|b|
44.
The distance of a point (x, y) from the origin is given by: —
sqrt(x^2 + y^2)
45.
The locus of a point equidistant from two fixed points is: —
The perpendicular bisector of the line segment joining the two points
46.
If point C divides the line segment AB internally in the ratio m:n, then the vector equation for C is given by: —
vec(c) = (n*vec(a) + m*vec(b))/(m+n)
47.
The distance between two points (x1, y1) and (x2, y2) is always non-negative. This is because: —
We take the square root of a sum of squares
48.
If the points (a, 0), (0, b), and (x, y) are collinear, then which of the following is true? —
x/a + y/b = 1
49.
The distance between two points (x1, y1) and (x2, y2) is zero if and only if: —
x1 = x2 and y1 = y2