PROJECT SINE - G10 - Q2-W7

Grade 10 - Q2-W7

By Jimmylyn Plurad

​PROJECT SINE

• APPLY THE DISTANCE FORMULA TO PROVE SOME GEOMETRIC PROPERTIES​

​MOST ESSENTIAL LEARNING COMPETENCIES​

DETERMINE THE LOCATION USING THE COORDINATES GIVEN.

WARM-UP ACTIVITY: WHERE AM I?

​

HI! BY THE WAY, I AM RYAN. MY MORNING ROUTINE IS TO JOG AROUND. I ENCOURAGE YOU TO EXERCISE WITH ME MENTALLY BY DETERMINING WHERE AM I USING THE COORDINATES I WILL BE GIVING. ARE YOU READY? LET US START!

WARM-UP ACTIVITY: WHERE AM I?

​

Multiple Choice

WHERE AM I IF THE COORDINATE OF MY EXACT LOCATION IS (10, 2)

• HOUSE

• MALL

• PARK

• CHURCH

Multiple Choice

WHERE AM I IF THE COORDINATE OF MY EXACT LOCATION IS (6, 5)

• HOUSE

• MALL

• PARK

• CHURCH

Multiple Choice

WHERE AM I IF THE COORDINATE OF MY EXACT LOCATION IS (4, 1)

• HOUSE

• MALL

• SCHOOL

• CHURCH

Multiple Choice

WHERE AM I IF THE COORDINATE OF MY EXACT LOCATION IS (3, 4)

• HOUSE

• MALL

• SCHOOL

• CHURCH

Multiple Choice

WHERE AM I IF THE COORDINATE OF MY EXACT LOCATION IS (7, 3)

• HOUSE

• MALL

• SCHOOL

• CHURCH

LET US OBSERVE!

​(10, 2)

​(7, 5)

​(5, 1)

​(3, 4)

​(7, 3)

​(3, 2)

LET'S US CONSIDER THE DIFFERENT LOCATIONS FROM RYAN'S COVERED PLACES AFTER JOGGING. LET US ASSUMED THAT EACH UNIT IN CARTESIAN PLANE IS ASSUMED TO BE 1 KILOMETER.

C​

H​

QUESTION 1:

HOW FAR IS THE CHURCH FROM THE HOSPITAL?​

LET US OBSERVE!

​(10, 2)

​(7, 5)

​(5, 1)

​(3, 4)

​(7, 3)

​(3, 2)

LET'S US CONSIDER THE DIFFERENT LOCATIONS FROM RYAN'S COVERED PLACES AFTER JOGGING. LET US ASSUMED THAT EACH UNIT IN CARTESIAN PLANE IS ASSUMED TO BE 1 KILOMETER.

C​

H​

QUESTION 1:

HOW FAR IS THE CHURCH FROM THE HOSPITAL?​

LET US OBSERVE!

​(10, 2)

​(7, 5)

​(5, 1)

​(3, 4)

​(7, 3)

​(3, 2)

LET'S US CONSIDER THE DIFFERENT LOCATIONS FROM RYAN'S COVERED PLACES AFTER JOGGING. LET US ASSUMED THAT EACH UNIT IN CARTESIAN PLANE IS ASSUMED TO BE 1 KILOMETER.

C​

H​

QUESTION 1:

HOW FAR IS THE CHURCH FROM THE HOSPITAL?​

LET US OBSERVE!

​(10, 2)

​(7, 5)

​(5, 1)

​(3, 4)

​(7, 3)

​(3, 2)

LET'S US CONSIDER THE DIFFERENT LOCATIONS FROM RYAN'S COVERED PLACES AFTER JOGGING. LET US ASSUMED THAT EACH UNIT IN CARTESIAN PLANE IS ASSUMED TO BE 1 KILOMETER.

C​

H​

QUESTION 1:

HOW FAR IS THE CHURCH FROM THE HOSPITAL?​

LET US OBSERVE!

​(10, 2)

​(7, 5)

​(5, 1)

​(3, 4)

​(7, 3)

​(3, 2)

C​

H​

QUESTION 2:

HOW FAR IS THE HOSPITAL FROM MALL?​

LET US OBSERVE!

​(10, 2)

​(7, 5)

​(5, 1)

​(3, 4)

​(7, 3)

​(3, 2)

C​

H​

QUESTION 2:

HOW FAR IS THE HOSPITAL FROM MALL?​

LET US OBSERVE!

​(10, 2)

​(7, 5)

​(5, 1)

​(3, 4)

​(7, 3)

​(3, 2)

C​

H​

QUESTION 2:

HOW FAR IS THE HOSPITAL FROM MALL?​

LET US OBSERVE!

​(10, 2)

​(7, 5)

​(5, 1)

​(3, 4)

​(7, 3)

​(3, 2)

C​

H​

QUESTION 2:

HOW FAR IS THE HOSPITAL FROM MALL?​

LET US OBSERVE!

​(10, 2)

​(7, 5)

​(5, 1)

​(3, 4)

​(7, 3)

​(3, 2)

C​

H​

QUESTION 3:

HOW FAR IS THE CHURCH FROM THE MALL?​

M

LET US OBSERVE!

​(10, 2)

​(7, 5)

​(5, 1)

​(3, 4)

​(7, 3)

​(3, 2)

C​

H​

QUESTION 3:

HOW FAR IS THE CHURCH FROM THE MALL?​

M

LET US OBSERVE!

​(10, 2)

​(7, 5)

​(5, 1)

​(3, 4)

​(7, 3)

​(3, 2)

C​

H​

QUESTION 3:

HOW FAR IS THE CHURCH FROM THE MALL?​

M

YES, IT IS RIGHT TRIANGLE.​

LET US OBSERVE!

​(10, 2)

​(7, 5)

​(5, 1)

​(3, 4)

​(7, 3)

​(3, 2)

C​

H​

QUESTION 2:

HOW FAR IS THE CHURCH FROM THE MALL?​

M

WHAT DO WE CALL SIDE MC OF THIS RIGHT TRIANGLE?​

LET US OBSERVE!

​(10, 2)

​(7, 5)

​(5, 1)

​(3, 4)

​(7, 3)

​(3, 2)

C​

H​

QUESTION 2:

HOW FAR IS THE CHURCH FROM THE MALL?​

M

MC = HYPOTENUSE​

FOR YOUR INFORMATION!

A​

C​

B​

FOR YOUR INFORMATION!

A​

C​

B​

FOR YOUR INFORMATION!

A​

C​

B​

FOR YOUR INFORMATION!

A​

C​

B​

FOR YOUR INFORMATION!

A​

C​

B​

Let's apply!

​(10, 2)

​(3, 4)

​(3, 2)

C​

H​

QUESTION 3: HOW FAR IS THE HOSPITAL FROM MALL?​

M

​M (3, 4)

Let's apply!

​(10, 2)

​(3, 4)

​(3, 2)

C​

H​

QUESTION 3: HOW FAR IS THE HOSPITAL FROM MALL?​

M

​M (3, 4)

​C (10, 2)

Let's apply!

​(10, 2)

​(3, 4)

​(3, 2)

C​

H​

QUESTION 3: HOW FAR IS THE HOSPITAL FROM MALL?​

M

​M (3, 4)

​C (10, 2)

Let's apply!

​(10, 2)

​(3, 4)

​(3, 2)

C​

H​

QUESTION 3: HOW FAR IS THE HOSPITAL FROM MALL?​

M

​M (3, 4)

​C (10, 2)

Let's apply!

​(10, 2)

​(3, 4)

​(3, 2)

C​

H​

QUESTION 3: HOW FAR IS THE HOSPITAL FROM MALL?​

M

​M (3, 4)

​C (10, 2)

Let's apply!

​(10, 2)

​(3, 4)

​(3, 2)

C​

H​

QUESTION 3: HOW FAR IS THE HOSPITAL FROM MALL?​

M

​M (3, 4)

​C (10, 2)

Let's apply!

​(10, 2)

​(3, 4)

​(3, 2)

C​

H​

QUESTION 4: HOW FAR IS THE SCHOOL FROM THE PARK?​

M

P ​(6, 5)

S ​(4, 1)

Let's apply!

​(10, 2)

​(3, 4)

​(3, 2)

C​

H​

QUESTION 4: HOW FAR IS THE SCHOOL FROM THE PARK?​

M

​P (6, 5)

​S (4, 1)

P ​(6, 5)

S ​(4, 1)

Let's apply!

​(10, 2)

​(3, 4)

​(3, 2)

C​

H​

QUESTION 4: HOW FAR IS THE SCHOOL FROM THE PARK?​

M

​P (6, 5)

​S (4, 1)

P ​(6, 5)

S ​(4, 1)

Let's apply!

​(10, 2)

​(3, 4)

​(3, 2)

C​

H​

QUESTION 4: HOW FAR IS THE SCHOOL FROM THE PARK?​

M

​P (6, 5)

​S (4, 1)

P ​(6, 5)

S ​(4, 1)

Let's apply!

​(10, 2)

​(3, 4)

​(3, 2)

C​

H​

QUESTION 4: HOW FAR IS THE SCHOOL FROM THE PARK?​

M

​P (6, 5)

​S (4, 1)

P ​(6, 5)

S ​(4, 1)

Let's apply!

​(10, 2)

​(3, 4)

​(3, 2)

C​

H​

QUESTION 4: HOW FAR IS THE SCHOOL FROM THE PARK?​

M

​P (6, 5)

​S (4, 1)

P ​(6, 5)

S ​(4, 1)

Let's apply!

​(10, 2)

​(3, 4)

​(3, 2)

C​

H​

QUESTION 4: HOW FAR IS THE SCHOOL FROM THE PARK?​

M

​P (6, 5)

​S (4, 1)

P ​(6, 5)

S ​(4, 1)

Let's apply!

​(10, 2)

​(3, 4)

​(3, 2)

C​

H​

QUESTION 4: HOW FAR IS THE SCHOOL FROM THE PARK?​

M

​P (6, 5)

​S (4, 1)

P ​(6, 5)

S ​(4, 1)

QUESTION : THE DISTANCE BETWEEN R(1, y) and S(5, 6) is 5.

Let's apply!

​

​

​

ACTIVITY 2:

GO THE DISTANCE

Multiple Choice

WHAT IS THE DISTANCE BETWEEN POINTS X(4, 7) AND Y(2, 3)

• $$\sqrt[]{5}$$  UNITS

• $$2\sqrt[]{5}$$  UNITS

• $$4\sqrt[]{5}$$  UNITS

• $$5\sqrt[]{2}$$  UNITS

Multiple Choice

WHAT IS THE DISTANCE BETWEEN POINTS X(5, 5) AND Y(8, -3)

• $$\sqrt[]{13}$$  UNITS

• $$2\sqrt[]{73}$$  UNITS

• $$\sqrt[]{73}$$  UNITS

• $$5\sqrt[]{5}$$  UNITS

Multiple Choice

A SEGMENT WHOSE ENDPOINTS ARE AT X(5, 5) AND Y(8, -3)

• $$x\ =-15\ or\ x=-1$$  

• $$x=-1\ or\ x=\ 15$$   

• $$x=1\ or\ x=-15$$  

• $$x=1\ or\ x=15$$  

​PROVE THAT THE DIAGONALS OF A RECTANGLE ARE CONGRUENT.

LET'S APPLY​:

​(0, 0)

A​

B​

C​

D​

​(A, 0)

​(a, b)

​(0, b)

​PROVE THAT THE DIAGONALS OF A RECTANGLE ARE CONGRUENT.

LET'S APPLY​:

​(0, 0)

A​

B​

C​

D​

​(A, 0)

​(a, b)

​(0, b)

​PROVE THAT THE DIAGONALS OF A RECTANGLE ARE CONGRUENT.

LET'S APPLY​:

​(0, 0)

A​

B​

C​

D​

​(A, 0)

​(a, b)

​(0, b)

​PROVE THAT THE DIAGONALS OF A RECTANGLE ARE CONGRUENT.

LET'S APPLY​:

​(0, 0)

A​

B​

C​

D​

​(A, 0)

​(a, b)

​(0, b)

​PROVE THAT THE DIAGONALS OF A RECTANGLE ARE CONGRUENT.

LET'S APPLY​:

​(0, 0)

A​

B​

C​

D​

​(A, 0)

​(a, b)

​(0, b)

​PROVE THAT THE DIAGONALS OF A RECTANGLE ARE CONGRUENT.

LET'S APPLY​:

​(0, 0)

A​

B​

C​

D​

​(A, 0)

​(a, b)

​(0, b)

​PROVE THAT THE DIAGONALS OF A RECTANGLE ARE CONGRUENT.

LET'S APPLY​:

​(0, 0)

A​

B​

C​

D​

​(A, 0)

​(a, b)

​(0, b)

​PROVE THAT THE DIAGONALS OF A RECTANGLE ARE CONGRUENT.

LET'S APPLY​:

​(0, 0)

A​

B​

C​

D​

​(A, 0)

​(a, b)

​(0, b)

​PROVE THAT THE DIAGONALS OF A RECTANGLE ARE CONGRUENT.

LET'S APPLY​:

​(0, 0)

A​

B​

C​

D​

​(A, 0)

​(a, b)

​(0, b)

​PROVE THAT THE DIAGONALS OF A RECTANGLE ARE CONGRUENT.

LET'S APPLY​:

​(0, 0)

A​

B​

C​

D​

​(A, 0)

​(a, b)

​(0, b)

​PROVE THAT THE OPPOSITE SIDES OF A RECTANGLE ARE CONGRUENT.

LET'S APPLY​:

​(0, 0)

A​

B​

C​

D​

​(A, 0)

​(a, b)

​(0, b)

LET'S APPLY​:

​(0, 0)

A​

B​

C​

D​

​(A, 0)

​(a, b)

​(0, b)

​PROVE THAT THE OPPOSITE SIDES OF A RECTANGLE ARE CONGRUENT.