Find the ratio in which the line segment joining the points (-3, 10) and (6, -8) is divided by the point (-1, 6).

Step 1: Define points and ratio

Let the given points be $A(-3, 10)$ and $B(6, -8)$. Let the point $P(-1, 6)$ divide the line segment $AB$ in the ratio $m_1 : m_2$. We need to find this ratio.

Step 2: Apply Section Formula for x-coordinate

We use the section formula to find the ratio. We can use either the $x$ -coordinate or the $y$ -coordinate. Let's start with the $x$ -coordinate. Substitute the values $x = -1$, $x_1 = -3$, and $x_2 = 6$ into the formula.

Step 3: Solve for the ratio using x-coordinates

Substitute the values into the section formula for the $x$ -coordinate. Then, cross-multiply and rearrange the terms to solve for the ratio $m_1 : m_2$. This gives us the ratio in which the point divides the line segment.

Step 4: Verify with y-coordinate (Optional)

To confirm our ratio, we can also apply the section formula using the $y$ -coordinates. Substitute $y = 6$, $y_1 = 10$, $y_2 = -8$, and the ratio $m_1 : m_2 = 2 : 7$ into the formula. Since both sides of the equation are equal, our ratio is correct.

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 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.
• Find the coordinates of a point P(x, y) lying on the line 2x + y = 6 such that the sum of its distances from the fixed points A(1, 1) and B(4, 5) is minimized

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