Unit 7 Lesson 2: Distance in the Coordinate Plane

Question 5

distance formula

Answer 5

a formula that uses the coordinates of two points to determine the distance between them on the coordinate plane

Question 6

line segment

Answer 6

part of a line that has two endpoints

Question 7

ordered pair

Answer 7

the two coordinates that name the location of a point on the coordinate plane

Question 8

Pythagorean Theorem

Answer 8

the theorem which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squared lengths of the other two sides

Question 9

x-coordinate

Answer 9

the first coordinate in an ordered pair that tells the distance to travel left or right from the origin

Question 10

y-coordinate

Answer 10

the second coordinate in an ordered pair that tells the distance to travel up or down from the origin

Question 11

What does the lenght of a line segment indicate

Answer 11

The distance between two points is the length of the line segment joining the two points.

Question 12

What can be the pytagoream throrem be used for

Answer 12

The Pythagorean Theorem can be used to find the distance between any two points in the coordinate plane.

Question 13

There is, in fact, a formula that can be used to determine the distance between any two points in the coordinate plane. This formula is called the

Answer 13

distance formula

Question 14

The distance formula is dervied from what

Answer 14

This formula is called the distance formula, which is derived from the Pythagorean Theorem.

Question 15

What is the distance formula equation

Answer 15

d=(x2−x1)2+(y2−y1)2−−−−−−−−−−−−−−−−−−√

Question 16

Does it matter which point is assigned to be (x1,y1)
and which is assigned to be (x2,y2)
?

Answer 16

The distance is the same regardless of which point is assigned to be (x1,y1)
and which is assigned to be (x2,y2)
. Because the differences between the x
and y
values are squared, it doesn’t matter whether that difference is positive or negative.

Question 17

Besides using the distance formula, how else can you determine the distance between any two points in the coordinate plane?

Answer 17

You can use the Pythagorean Theorem to find the distance between any two points in the coordinate plane.

Question 18

Explain how the distance formula works based on what you know about the Pythagorean Theorem.

Answer 18

In the Pythagorean Theorem, square the lengths of two legs of a triangle and add them together to find the squared length of the hypotenuse of a triangle. In order to derive the distance formula, create a triangle. You are trying to find the distance between two points of a line segment. This is the hypotenuse of a triangle. Calculate the square root of the sum of the lengths of the legs of the triangle in order to find the length of the line segment.

Question 19

What part of a triangle could you assume line segment RS¯¯¯¯¯
creates in order to use the distance formula to solve for the distance between points R(−5,8)
and S(3,−4)
on a coordinate plane?

Answer 19

The distance formula could assume RS¯¯¯¯¯
is the hypotenuse of a triangle.

Question 20

What is the distance between the points Q(−2,4)
and P(7,−2)
, to the nearest tenth? Use the distance formula to find your answer. Show your work.

Answer 20

d=====((−2)−7)2+(4−(−2))2−−−−−−−−−−−−−−−−−−−−−√(−9)2+62−−−−−−−−−√81+36−−−−−−√117−−−√10.8

Question 21

adjacent sides

Answer 21

two sides of a polygon that share a common vertex

Question 22

perimeter

Answer 22

the continuous line forming the boundary of an enclosed geometric figure

Question 23

vertex

Answer 23

the point where two adjacent sides of a polygon meet; the plural of vertex is vertices

Question 24

How to find the perimetor od a paralleogram

Answer 24

since parallelograms have opposite sides that are equal in length, you need only find the length of a pair of adjacent sides to know the lengths of all four sides. The perimeter of a parallelogram is the sum of 2 times one side length and 2 times the adjacent side length.

Question 25

How can you calculate the perimeter of a polygon on a coordinate plane given the coordinates of its vertices?

Answer 25

If you know the coordinates of the vertices of the polygon, you can graph them on a coordinate plane. Then, calculate the distance of each line segment that make up the perimeter of the polygon. Add all of these distances together to find the perimeter.

Question 26

What is the perimeter of the triangle with vertices A(−2,−2)
, B(3,1)
, and C(1,−3)
? If needed, round each side length to the nearest tenth.

Answer 26

AB====≈(3−(−2))2+(1−(−2))2−−−−−−−−−−−−−−−−−−−−−√52+32−−−−−−√25+9−−−−−√34−−√5.8

BC====≈(1−3)2+((−3)−1)2−−−−−−−−−−−−−−−−−−√(−25)2+(−4)2−−−−−−−−−−−−√4+16−−−−−√20−−√4.5

AC====≈(1−(−2))2+((−3)−(−2))2−−−−−−−−−−−−−−−−−−−−−−−√32+(−1)2−−−−−−−−−√9+1−−−−√10−−√3.2

Perimeter = 5.8 + 4.5 + 3.2 = 13.5