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# Point P(X, 4) Lies on the Line Segment Joining the Points A(−5, 8) and B(4, −10). Find the Ratio in Which Point P Divides the Line Segment Ab. Also Find the Value of X. - CBSE Class 10 - Mathematics

ConceptConcepts of Coordinate Geometry

#### Question

Point P(x, 4) lies on the line segment joining the points A(−5, 8) and B(4, −10). Find the ratio in which point P divides the line segment AB. Also find the value of x.

#### Solution

Let point P (x, 4) divide line segment AB in the ratio K:1.

Coordinates of A = (−5, 8)

Coordinates of B = (4, −10)

On using section formula, we obtain

(x,4)=((kxx4+1xx(-5))/(k+1))((kxx(-10)+1xx8)/(k+1))

(x,4)=((4k-5)/(k+1),(-10k+8)/(k+1))

rArr(4k-5)/(k+1)=x........................(1)

and (-10k+8)/(k+1)=4..................(2)

From equation (2):

− 10K + 8 = 4(K + 1)

⇒ − 10K + 8 = 4K + 4

⇒ 14K = 4

rArr K =2/7

Thus, point P divides AB in the ratio 2/7 : ie ., 2:7.

From equation (1):

(4xx2/7-5)/(2/7+1)=x

(-27/7)/(9/7)=x

x=-3`

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Solution Point P(X, 4) Lies on the Line Segment Joining the Points A(−5, 8) and B(4, −10). Find the Ratio in Which Point P Divides the Line Segment Ab. Also Find the Value of X. Concept: Concepts of Coordinate Geometry.
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