Calculating Midpoint Coordinates
To find the midpoint of a line segment, we use the midpoint formula. This formula averages the x-coordinates and the y-coordinates of the two endpoints.
The midpoint formula is given by:
\(M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)\)
Identify Endpoint Coordinates
The two given points are \((-2, -1)\) and \((-5, -3)\).
- Let \((x_1, y_1) = (-2, -1)\)
- Let \((x_2, y_2) = (-5, -3)\)
Calculate Midpoint X-Coordinate
Substitute the x-values into the formula:
\(x_m = \frac{x_1 + x_2}{2} = \frac{-2 + (-5)}{2} = \frac{-2 - 5}{2} = \frac{-7}{2}\)
Calculate Midpoint Y-Coordinate
Substitute the y-values into the formula:
\(y_m = \frac{y_1 + y_2}{2} = \frac{-1 + (-3)}{2} = \frac{-1 - 3}{2} = \frac{-4}{2} = -2\)
Determine Midpoint
Combining the calculated coordinates, the midpoint is:
\(\left( \frac{-7}{2}, -2 \right)\)
This corresponds to the second option.
Similar Questions
- \(A(1, 2)\), \(B(a, -26)\), \(C(13, -14)\) and \(D(6, 14)\) are the vertices of a parallelogram, taken in order, find the value of \(a\).
- What would be the area of the triangle with \(A(8, 8)\), \(B(22, 8)\) and \(C(16, -10)\) as vertices?
- What would be the point which divides the line segment connecting the points \(P(10, 18), Q(5, 8)\) in the ratio \(2 : 3\) internally
- Find a point on the X axis which is equidistant from A(2, -3) and B(-2, 1)
- If point C is equidistant from A(5, -6) and B(7, 8), coordinate of C will be
- The area of the triangle whose vertices are given by (2, 4), (– 3, – 1) and (5, 3) is:
Important Questions from Coordinate Geometry
Find the co-ordinates of the centroid of a triangle whose vertices are A(1, 4), B(7, 8) and C(10, 12).
- If x² + y² - 16x + 38y + 425 = 0, then the value of x² + y² is:
- If x² + y² - 12x + 18y + 117 = 0, then the value of x² + y² is:
- A geological survey team has established three research stations forming a triangular monitoring zone. The stations are located at coordinates P(2,5), Q(8,1), and R(4,9) on a coordinate grid where each unit represents 1 kilometer. What is the area of the triangular monitoring zone?
- \(A(1, 2)\), \(B(a, -26)\), \(C(13, -14)\) and \(D(6, 14)\) are the vertices of a parallelogram, taken in order, find the value of \(a\).
