QuestionFind the coordinate of $Q$ on $\overline{F L}$ where the ratio $FQ:QL$ is $12:7$ , with $F = -15$ and $L = 4$ .

Studdy Solution

STEP 1

Assumptions1. The line segment $\overline{ L}$ is a straight line on a number line. . Point $is at coordinate -15.<br />3. Point$ is at coordinate4.
4. Point $Q$ is somewhere between $and$ such that the ratio of $Q$ to $Q L$ is $127$ .

STEP 2

First, we need to find the total length of the line segment $\overline{ L}$ .
$Length_{FL} = L - F$

STEP 3

Now, plug in the given values for the coordinates of $and$ to calculate the length of $\overline{ L}$ .
$Length_{FL} = - (-15)$

STEP 4

Calculate the length of $\overline{ L}$ .
$Length_{FL} =4 +15 =19$

STEP 5

The length of $\overline{ Q}$ to $\overline{Q L}$ is in the ratio $127$ . This means that the total length of $\overline{ L}$ is divided into12 parts and7 parts. So, the total parts is $12 +7 =19$ parts.

STEP 6

Each part of the line segment $\overline{ L}$ is equal to the total length of $\overline{ L}$ divided by the total number of parts. $Length_{part} = Length_{FL} / Total\, parts$

STEP 7

Plug in the values for the length of $\overline{ L}$ and the total number of parts to calculate the length of each part.
$Length_{part} =19 /19$

STEP 8

Calculate the length of each part.
$Length_{part} =19 /19 =1$

STEP 9

The length of $\overline{ Q}$ is equal to the length of each part multiplied by the number of parts in $Q$ , which is12.
$Length_{Q} = Length_{part} \\times Parts_{Q}$

STEP 10

Plug in the values for the length of each part and the number of parts in $Q$ to calculate the length of $\overline{ Q}$ .
$Length_{Q} = \\times12$

STEP 11

Calculate the length of $\overline{ Q}$ .
$Length_{Q} = \\times =$

STEP 12

The coordinate of $Q$ is equal to the coordinate of $$ plus the length of $\overline{ Q}$.
$Q = F + Length_{Q}$

STEP 13

Plug in the values for the coordinate of $$ and the length of $\overline{ Q}$ to calculate the coordinate of $Q$.
$Q = -15 +12$

STEP 14

Calculate the coordinate of $Q$ .
$Q = - +12 = -3$ The coordinate of $Q$ is -3.

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms