Question

what is the distance between point l and the origin? 9 units
what is the distance between point m and the origin? 5 units
what is the distance between point l and point m? 4 units
how can you find the distance between point l and point m? ? the distances between each point and the origin.

Explanation:

To solve the problem of finding how to determine the distance between point \( L \) and point \( M \) using their distances to the origin, we can use the following reasoning:

Step 1: Identify the distances from each point to the origin

• The distance from point \( L \) to the origin (let's call this \( d_L \)) is given as 9 units.
• The distance from point \( M \) to the origin (let's call this \( d_M \)) is given as 5 units.

Step 2: Determine the distance between \( L \) and \( M \)

Since both points lie on the x - axis (their y - coordinates are 0), the distance between them can be found by taking the absolute difference of their distances from the origin. Mathematically, if two points \( x_1 \) and \( x_2 \) lie on the x - axis, the distance between them is \( |x_1 - x_2| \). Here, the distance of \( L \) from the origin is \( x_1=9 \) (since it's at \( (9,0) \)) and the distance of \( M \) from the origin is \( x_2 = 5\) (since it's at \( (5,0) \)). So the distance between \( L \) and \( M \) is \( |9 - 5|=4 \) units, and the way to find it using their distances to the origin is to subtract the smaller distance from the larger distance (or take the absolute difference of their distances from the origin).

For the last part of the question "How can you find the distance between point \( L \) and point \( M \)?... the distances between each point and the origin." The operation we use is to subtract (or find the absolute difference of) the two distances. So we fill in the blank with "Subtract" (or "Find the absolute difference of").

Final Answers:

• Distance between \( L \) and origin: \( \boldsymbol{9} \) units.
• Distance between \( M \) and origin: \( \boldsymbol{5} \) units.
• Distance between \( L \) and \( M \): \( \boldsymbol{4} \) units.
• To find the distance between \( L \) and \( M \) using their distances to the origin, we \(\boldsymbol{\text{subtract}}\) (or find the absolute difference of) the two distances.

Answer:

To solve the problem of finding how to determine the distance between point \( L \) and point \( M \) using their distances to the origin, we can use the following reasoning:

Step 1: Identify the distances from each point to the origin

• The distance from point \( L \) to the origin (let's call this \( d_L \)) is given as 9 units.
• The distance from point \( M \) to the origin (let's call this \( d_M \)) is given as 5 units.

Step 2: Determine the distance between \( L \) and \( M \)

Since both points lie on the x - axis (their y - coordinates are 0), the distance between them can be found by taking the absolute difference of their distances from the origin. Mathematically, if two points \( x_1 \) and \( x_2 \) lie on the x - axis, the distance between them is \( |x_1 - x_2| \). Here, the distance of \( L \) from the origin is \( x_1=9 \) (since it's at \( (9,0) \)) and the distance of \( M \) from the origin is \( x_2 = 5\) (since it's at \( (5,0) \)). So the distance between \( L \) and \( M \) is \( |9 - 5|=4 \) units, and the way to find it using their distances to the origin is to subtract the smaller distance from the larger distance (or take the absolute difference of their distances from the origin).

For the last part of the question "How can you find the distance between point \( L \) and point \( M \)?... the distances between each point and the origin." The operation we use is to subtract (or find the absolute difference of) the two distances. So we fill in the blank with "Subtract" (or "Find the absolute difference of").

Final Answers:

• Distance between \( L \) and origin: \( \boldsymbol{9} \) units.
• Distance between \( M \) and origin: \( \boldsymbol{5} \) units.
• Distance between \( L \) and \( M \): \( \boldsymbol{4} \) units.
• To find the distance between \( L \) and \( M \) using their distances to the origin, we \(\boldsymbol{\text{subtract}}\) (or find the absolute difference of) the two distances.