The document is a mathematics worksheet that contains questions about using the distance formula to calculate distances between points on a coordinate plane. It includes examples of using the distance formula, finding midpoints of line segments, and identifying geometric shapes formed by connecting points. It then provides 10 multiple choice questions testing understanding of using the distance formula, finding midpoints, and applying coordinate plane concepts.

1. Name: ____________________________________________________________________
Grade and Section: ________________________ Date: _______________________
Subject: MATHEMATICS 10_____Subject Teacher: _________________________________
WORKSHEET NO.1
FOURTH QUARTER
Learning Competency: M10GE-IIg-2. Applies the distance formula to prove some
geometric properties.
Perform the following activity. Answer every question that follows.
1. Plot the points A (2,1) and B (8,9) on the coordinate plane below.
2. Draw a horizontal line passing through A and a vertical line containing B.
3. Mark and label the point of intersection of the two lines as C.
What are the coordinates of C? Explain how you obtained your answer.
What is the distance between A and C?
How about the distance between B and C?
4. Connect A and B by a line segment.
What kind of triangle is formed by A, B, and C? Explain your answer.
How will you find the distance between A and B?
What is AB equal to?
Distance between Two Points
The distance between two points is always nonnegative. It is positive when the two
points are different, and zero if the points are the same. If P and Q are two points,
then the distance from P to Q is the same as the distance from Q to P. That is, PQ =
QP.
The Distance Formula
The distance between two points, whether they are aligned horizontally or vertically,
can be determined using the distance formula.
Consider the points P and Q whose coordinates are (x1, y1) and (x2, y2 ) respectively.
The distance d between these points can be determined using the distance formula
d = √(x2- x1)2 + (y2- y1)2 or PQ = √(x2- x1)2 + (y2- y1)2
EXAMPLE1: Find the distance between P (1, 3) and Q (7, 11).
Solution: To find the distance between P and Q, the followingprocedures can be followed.

2. The distance formula has many applications in real life. It can be used to find the
distance between two objects or places.
Example 3: A map showing the locations of different municipalities and cities is drawn
on a coordinate plane. Each unit on the coordinate plane is equivalent to 6 kilometers.
Suppose the coordinates of Mabini City is (2, 2) and Sta. Lucia town is (6, 8). What is
the shortest distance between these two places?

3. Activity 1: Find the distance between each pair of points on the coordinate plane.
Activity #2: Find the coordinates of the midpoint of the segment whose endpoints
are given below.

4. Name: ____________________________________________________________________
Grade and Section: ________________________ Date: _______________________
Subject: MATHEMATICS 10_____Subject Teacher: _________________________________
LAS #3:
Read each question carefully and write the letter of the correct answer on a sheet of
paper (1 whole).
1. Which of the following represents the distance d between the two points
(x1, y1) and (x2, y2) ?
a. d = √(x2 + x1)2 + (y2 + y1)2 c. d = √(x2- x1)2 + (y2- y1)2
b. d = √(x2 + x1)2- (y2 + y1)2 d. d = √(x2- x1)2- (y2- y1)2
2. What is the distance between the points M (-3,1) and N (7, -3)?
a. 6 b. 2√29 c. 14 d. 4√29
3. Which of the following represents the midpoint M of the segment whose
endpoints are (x1, y1) and (x2, y2)?
a. M = (
x1- x2
2
,
y1- y2
2
) c. M = (
x1+y1
2
,
x2+ y2
2
)
b. M = (
x1+ x2
2
,
y1+ y2
2
) d. M = (
x1- y1
2
,
x2- y2
2
)
4. What are the coordinates of the midpoint of a segment whose endpoints are
(-1, -3) and (11, 7)?
a. (2, 5) b. (6, 5) c. (-5, -2) d. (5, 2)
5. P and Q are points on the coordinate plane as shown in the figure below.
If the coordinates of P and Q are (-2,5) and (8,5), respectively, which of the
following would give the distance between the two points?
a. |-2-5| b. |8-5| c. |8-2| d. |-2-8|
6. Point L is the midpoint of 𝐾𝑀
̅̅̅̅̅ . Which of the following is true about the
distances among K, L, and M?
a. KL=KM c. KL=LM
b. LM=KM d. 2|KM| = KL + LM
7. What figure is formed when the points A(3, 7), B(11, 10), C(11, 5), and D(3, 2) are
connected consecutively?
a. Parallelogram c. square
b. Trapezoid d. rectangle
8. A map is drawn on a grid where 1 unit is equivalent to 1 km. On the same map,
the coordinates of the point corresponding to San Vicente is (4, 9). Suppose San
Vicente is 13 km away from San Luis. Which of the following could be
coordinates of the point corresponding to San Luis?
a. (-13, 0) b. (16, 4) c. (4, 16) d. (0, 13)
9. What are the coordinates of the midpoint of a segment whose endpoints are
A (6, 8) and B (12, 10)?
a. (8,8) b. (8,9) c. (9, 8) d. (9,9)
10. Find the distance between M (2, -3) and N (10, -3)?
a. 4 b. 5 c. 6 d. 7