Find the ratio in which P(4, m) divides the line segment joining the points A(2, 3) and B(6, -3). Hence, find m.

Step 1: Apply Section Formula for x-coordinate

We use the section formula to find the ratio in which point P divides the line segment AB. Let the ratio be $k:1$. The coordinates of point P are $(x, y)$, and the coordinates of points A and B are $(x_1, y_1)$ and $(x_2, y_2)$ respectively. We substitute the given $x$ -coordinates into the formula.

Step 2: Calculate the ratio k

Substitute the given $x$ -coordinates: $x=4$, $x_1=2$, and $x_2=6$ into the section formula. Then, solve the equation for $k$. This gives us the ratio in which P divides AB.

Step 3: State the ratio

Since we found $k=1$, the ratio in which P divides the line segment AB is $1:1$. This means P is the midpoint of AB.

Step 4: Apply Section Formula for y-coordinate

Now we use the section formula for the $y$ -coordinate to find the value of $m$. We already know the ratio $k=1$, and the $y$ -coordinates of A and B are $y_1=3$ and $y_2=-3$ respectively. The $y$ -coordinate of P is $m$.

Step 5: Calculate m

Substitute $k=1$, $y_1=3$, and $y_2=-3$ into the section formula for the $y$ -coordinate. Perform the arithmetic to find the value of $m$.

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.

All Coordinate Geometry solutions →