Question

Which shows how to find the x-coordinate of the point that will divide AB into a 2:3 ratio using the formula x= (x2−x1)⋅r+x1⋅s/r+s?

a) x= (−3−2)+2/3-2
b) x= (2+3)−3/3-2
c) x= (−3−1)/(3-2)
d) x= (2+3)−3/2+3

Answer 1

To find the x-coordinate of the point that divides AB in a 2:3 ratio, substitute the given values into the formula x = (x2 - x1) * r + x1 * s / (r + s). The correct option is b) x = (2 + 3) - 3 / (3 - 2), which simplifies to x = 2.

Step-by-step explanation:

To find the x-coordinate of the point that will divide AB into a 2:3 ratio using the formula x = (x2 - x1) * r + x1 * s / (r + s), you need to substitute the given values into the formula. In this case, the correct option is b) x = (2 + 3) - 3 / (3 - 2). By substituting the values, we get x = 5 - 3 / 1, which simplifies to x = 2.

Answer 2

The expression to find the x-coordinate using the formula
`\(x = ((x_2 - x_1) \cdot r + x_1 \cdot s)/(r + s)\)` is represented by option b)
`\(x = ((2 + 3) - 3)/(3 - 2)\).`

Step-by-step explanation:

The given formula is used to find the x-coordinate of a point that divides a line segment AB into a given ratio, where
`\(r\) and \(s\)` are the ratios. In this case, the formula
`\(x = ((x_2 - x_1) \cdot r + x_1 \cdot s)/(r + s)\)` is utilized. To understand the application, let's break down the correct expression in option b:

`\[x = ((2 + 3) - 3)/(3 - 2)\]`

Here,
`\(x_1\) is 2, \(x_2\) is 3, \(r\) is 2, and \(s\)` is 3. Plugging these values into the formula gives the correct expression for finding the x-coordinate.

It's important to note that the denominator
`\(r + s\)` in the formula is a sum of the ratio values, and the numerator
`\((x_2 - x_1) \cdot r + x_1 \cdot s)\)`involves the multiplication of differences in x-coordinates with the corresponding ratio values. The correct application of this formula ensures an accurate determination of the x-coordinate that satisfies the given ratio conditions for dividing the line segment AB.

So correct option is option b)