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Hotmath Practice Problems

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Title:
Hotmath Algebra 2
Author:
Hotmath Team
 
Free
Chapter:Quadratic Relations/Analytic GeometrySection:The Distance Formula and the Midpoint Formula
 

Problem: 1

Find the distance between the two points.

(–5, 8), (0, –4)

 

Problem: 3

Find the distance between the two points.

 

Problem: 5

Find the distance between points (p, q) and (0, q).

 

Problem: 7

Find the midpoint of the line segment connecting

(6, 5) and (12, 9).

 

Problem: 9

Find the midpoint of the line segment connecting

(0.25, 4) and (–0.9, –2).

 

Problem: 11

Determine the distance between the two points and then determine the midpoint of the line segment joining the two points.

(0, 0), (6, 8)

 

Problem: 13

Determine the distance between the two points and then determine the midpoint of the line segment joining the two points.

(–4.5, 2.4), (8, –4.6)

 

Problem: 15

Determine the distance between the two points and then determine the midpoint of the line segment joining the two points.

(–9, 4), (–13/2, 6)

 

Problem: 17

Determine the distance between the two points and then determine the midpoint of the line segment joining the two points.

{(2 + √ 5), (3 + √ 3)} and {(2 – √ 5), (–1 + sqrt 3)}.

 

Problem: 19

The distance between the given points is 13 units. Find the value of a.

(– 7, 3), (a, 15)

 

Problem: 21

Solve for x using the given distance d between the two points.

 

Problem: 23

M is the midpoint of PQ. Find the coordinates of Q.

P(1, 1), M(3, 5)

 

Problem: 25

The coordinates of one endpoint of the line segment XY and the midpoint M is given. Find the coordinates of the other end point.

M(0.55, 2.95), X(2.1, 3.9)

 

Problem: 27

Classify the triangle as scalene, isosceles, or equilateral from the given vertices.

(7, 0), (3, –4), (8, –5)

 

Problem: 29

Classify the triangle as scalene, isosceles, or equilateral from the given vertices.

(4, 7), (6, 2), (5, –2)

 

Problem: 31

The coordinates of vertices of δABC are given. Classify the triangle on basis of the length of its sides. Also check if it is a right triangle. If it is right triangle, find the area of the triangle.

A(–1, 3), B(3, 2) and C(2, –2).

 

Problem: 33

The coordinates of vertices of δABC are given. Classify the triangle on basis of the length of its sides. Also check if it is a right triangle. If it is right triangle, find the area of the triangle.

A(6, –3), B(–2, 5) and C(–1, –2).

 

Problem: 35

Coordinates of three points are given. Determine if the points are collinear.

Hint: If distance between one pair of points is sum of the distances between the other pair of points, then the points are collinear.

A(2, 3), B(8, 5) and C(–1, 2).

 

Problem: 37

Coordinates of three points are given. Determine if the points are collinear.

Hint: If distance between one pair of points is sum of the distances between the other pair of points, then the points are collinear.

A(–4, –1), B(–1, 2) and C(2, 4).

 

Problem: 39

Write an equation for the perpendicular bisector of the line segment joining the two points: (4, 4), (8, 20)

 

Problem: 41

Give an equation for the perpendicular bisector of the line segment joining the two points:

(–4, –9.2), (–5.2, 2.8)

 

Problem: 43

Find the points on the coordinate axes that are equidistant from the the points

A(–1, 0) and B(0, 3).