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Distance Formula Applications Worksheet

1) The document is a mathematics worksheet that provides 15 problems involving using the distance formula and coordinates to analyze geometric shapes and scenarios on a coordinate plane. 2) The problems involve determining if points are collinear, calculating distances between points, classifying triangles by their angles and sides, finding perimeters and areas of rectangles, verifying quadrilateral types, and applying scale factors to real-world maps and diagrams. 3) Solving the problems requires using the distance formula, plotting points, sketching shapes, and performing calculations to analyze geometric relationships between coordinates.

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Reymund Gonowon
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90 views2 pages

Distance Formula Applications Worksheet

1) The document is a mathematics worksheet that provides 15 problems involving using the distance formula and coordinates to analyze geometric shapes and scenarios on a coordinate plane. 2) The problems involve determining if points are collinear, calculating distances between points, classifying triangles by their angles and sides, finding perimeters and areas of rectangles, verifying quadrilateral types, and applying scale factors to real-world maps and diagrams. 3) Solving the problems requires using the distance formula, plotting points, sketching shapes, and performing calculations to analyze geometric relationships between coordinates.

Uploaded by

Reymund Gonowon
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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Mathematics 11 Topic:

WORKSHEET # 1.1
1st Trimester Distance Between Two Points

Directions: Analyze the situations and perform the instructions provided.

1. HW Using the distance formula, how do we show that three points are collinear? Which set of three coordinates from A ( 0,0 ) ,
B (−2,8 ) , C ( 3,2 ) , D (1,−4 ) , and E (−9 ,−6 ) , are collinear?

2. If the distance from ( x,−2 ) and ( 2,4 ) is 10 units, what is the value of x if it is located on the third quadrant? How would you
solve for the value of x?

3. The coordinates ( 2,6 ) and ( 7,−2 ) are both equidistant from (−3, y ) . In which quadrant(s) is (−3, y ) located? What
is/are the value(s) of y?

4. The vertices of triangle ABC are A (−2,−3 ) , B ( 2,1 ) , and C (−6,5 ) .


a. Plot the vertices and sketch the triangle on the coordinate plane on the right.
b. If 1 unit = 1 cm, what is the perimeter of Δ ABC ? Explain how you would
determine the perimeter given the coordinates of this triangle.

5. Triangle DEF has vertices at D ( 4,1 ) , E ( 1,−2 ) , and F ( 6,−4 ) .


a. Plot the vertices and sketch the triangle on the coordinate plane on the right.
b. Is the triangle scalene, isosceles, or equilateral? Explain your answer.

6. HW Triangle GHI has vertices at G ( 5,−2 ) , H (1,1 ) , and I ( 7,9 ) .


a. Plot the vertices and sketch the triangle on the coordinate plane on the right.
b. How do we verify if ΔGHI is acute, obtuse, or a right triangle? Classify ΔGHI .

7. If the coordinates ( 5,4 ) , (−5,8 ) , (−7,3 ) , and ( 3,−1 ) form a rectangle, what is the perimeter and area of this rectangle?
How do we determine the perimeter and area of a rectangle using the distance formula?

8. HW Verify the type of quadrilateral whose vertices are the coordinates (−2,7 ) , ( 5,4 ) , (−8,−7 ) , and (−1,−10 ) . Explain
how the distance formula aids in classifying this quadrilateral.

9. A diagonal of a quadrilateral has the endpoints ( 2,−4 ) , and ( 6,−2 ) . If the quadrilateral is a rectangle, provide two possible
coordinates which are the endpoints of the other diagonal. Explain how you obtained the coordinates.

10. Determine if the coordinates (−2,3 ) , (−2,−1 ) , ( 4 ,−1 ) , and ( 4,3 ) are equidistant from ( 1,1 ) . What geometric figure is
best suited to represent all points equidistant from ( 1,1 ) ?

Worksheet # 1.1 Page | 1


Mathematics 11
1st Trimester
Mr. Reymund Gonowon
11. A circle, whose center is at (−2,3) , has a radius the measures 5 units. Identify whether the following points are located at the
interior of the circle, exterior of the circle, or on the circle. Explain how the distance formula is used to complete this task.

12. The coordinate plane at the right shows a map for a vacation trip. Each square grid has a side
that represents 50 miles. During your vacation, you want to visit all of the sites on the map.
There are two orders in which to visit the sites so that you travel the shortest distance. What
are these two orders?

⃗ ⃗
13. The diagram shows existing roads BD and DE , and a planned new road CE under
⃗
construction. How much shorter is the trip going to be from B to E after the construction

of the new road


⃗
CE ?

14. The map below is a route for a hike. At present, rough weather is occurring and the hiker needs
to find a place to settle as soon as possible. If the hiker is already at point B, would you
recommend for him to go to point A and settle there or to make his way to the lodge?

15. A photo of a crater on Mars was taken and shown here. It takes a circular shape and the two
points that are indicated are endpoints of the diameter. If the photo uses a scale of I unit = 1
kilometer, what is the circumference of this crater?

Worksheet # 1.1 Page | 2


Mathematics 11
1st Trimester
Mr. Reymund Gonowon

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