Question

Douglas has a segment with endpoints I(5, 2) and J(9, 10) that is divided by a point K such that IK and KJ form a 2:3 ratio. He knows that the distance between the x-coordinates is 4 units. Which of the fractions below will let him find the x-coordinate for point K? A. 2/3 B. 2/5 C. 3/2 D. 3/5

Answer 1

Answer: B. 2/5

Explanation:

According to the question,

Douglas has a segment with endpoints I(5, 2) and J(9, 10) that is divided by a point K such that IK and KJ form a 2:3 ratio.

For finding the x-coordinate of K, the following steps can be used,

Step 1: Find the length of line segment IJ.

For this we will find the difference between the x-coordinates of points (5,2) and (9,10)

Which is 4. ( Because, 9 - 5 = 4 )

Step 2 : Find the length of IK, For this, Multiply the difference by the fraction 2/5.

`( IK:KJ=2:3 \implies IK =(2)/(2+3)IJ=(2)/(5)IJ)`

`\text{Hence, }IJ = (2)/(5)* 4=(8)/(5)`

Step 3: Now add IJ with the x-coordinate of point I,

`\text{Thus, the x- coordinate of point K}= 5 + (8)/(5)=(25+8)/(5)=(33)/(5)`

Hence, Option B is correct.

Answer 2

B
This is because the segement IK contains 2 parts of the total 5 parts in which the segment IJ has been divided. Therefore, multiplying by 2/5 will help Douglas find the x-coordinate of K.