Find the ratio in which the point $(-1, k)$ divides the line segment joining the points $(-3, 10)$ and $(6, -8)$. Hence, find the value of k.

Step 1: Apply Section Formula for x-coordinate

Let the point $P(-1, k)$ divide the line segment joining $A(-3, 10)$ and $B(6, -8)$ in the ratio $m_1 : m_2$. We use the section formula for the $x$ -coordinate to find this ratio. Here, $x = -1$, $x_1 = -3$, and $x_2 = 6$.

Step 2: Calculate the ratio

Substitute the given values into the section formula for the $x$ -coordinate and solve for the ratio $m_1 : m_2$. This gives us the ratio in which the point divides the line segment.

Step 3: Apply Section Formula for y-coordinate

Now that we have the ratio $m_1 : m_2 = 2 : 7$, we can use the section formula for the $y$ -coordinate to find the value of $k$. Here, $y = k$, $y_1 = 10$, and $y_2 = -8$.

Step 4: Calculate the value of k

Substitute the ratio $m_1 = 2$, $m_2 = 7$, and the $y$ -coordinates into the section formula. Perform the arithmetic to find the value of $k$.

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]
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• 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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