A line segment joining the points P(-5, 11) and Q is divided internally by the point M(2, -3) such that PM : MQ = 7 : 2. The coordinates of Q are :

Step 1: Understand the Section Formula

The section formula is used to find the coordinates of a point that divides a line segment in a given ratio. Here, point M divides the line segment PQ in the ratio $m:n = 7:2$. We are given the coordinates of P and M, and we need to find the coordinates of Q.

Step 2: Identify Given Values

Let the coordinates of P be $(x_1, y_1)$, the coordinates of M be $(x, y)$, and the coordinates of Q be $(x_2, y_2)$. The given ratio is $m:n = 7:2$. We need to find $(x_2, y_2)$.

Step 3: Apply Section Formula for x-coordinate

Substitute the known values into the section formula for the $x$ -coordinate. We have $x=2$, $m=7$, $n=2$, and $x_1=-5$. We will solve this equation for $x_2$.

Step 4: Solve for $x_2$

Simplify the equation and solve for $x_2$. Multiply both sides by 9, then add 10 to both sides, and finally divide by 7 to find the value of $x_2$.

Step 5: Apply Section Formula for y-coordinate

Similarly, substitute the known values into the section formula for the $y$ -coordinate. We have $y=-3$, $m=7$, $n=2$, and $y_1=11$. We will solve this equation for $y_2$.

Step 6: Solve for $y_2$

Simplify the equation and solve for $y_2$. Multiply both sides by 9, then subtract 22 from both sides, and finally divide by 7 to find the value of $y_2$.

Step 7: State the Coordinates of Q

Combining the calculated $x_2$ and $y_2$ values, the coordinates of point Q are $(4, -7)$.

More from this chapter

• Q7. If A(a, 0), B(1, 1) and C(0, b) form a triangle, right angled at B when joined, then establish a relation between a and b. [2 Marks]
• Find the ratio in which the line segment joining the points (-3, 10) and (6, -8) is divided by the point (-1, 6).
• Find a point on the y-axis that is at the same distance from the points (-5, 2) and (9, -2).
• Find the coordinates of the point which divides the line segment joining (4, -3) and (8, 5) in the ratio 3:1 internally.
• Find the relation between x and y if the point (x, y) is equidistant from (7, 1) and (3, 5).
• 1. Find the distance between the following pairs of points: (i) (2, 3), (4, 1) (ii) (-5, 7), (-1, 3) (iii) (a, b), (-a, -b)
• Find the coordinates of the points of trisection of the line segment joining the points A(2, -2) and B(-7, 4).
• Find the ratio in which the line segment joining A(1, -5) and B(-4, 5) is divided by the x-axis, and find the coordinates of the point of division.

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