#### The straight line l_1 with equation y = \frac{2}{3}x - 2 crosses the y-axis at the point P. The point Q has coordinates (5, −3).

Calculate the coordinates of the mid-point of PQ.

Anonymous

0

Calculate the coordinates of the mid-point of PQ.

Krishna

0

Step 1: Find the coordinate (x or y) at the point of intersection:

NOTE: If the line intersecting the y-axis then put x = 0 in the equation

If the line intersecting the x-axis then put y = 0 in the equation.

Step 2: Note down the given values and understand hints given

Step 3: Calculate the any one endpoint of the line by using the hints

NOTE: i) Either line crossing the x axis means y = 0, or

line crossing the y-axis means x = 0, substituting in the line equation.

Step 4: Substitute the values of midpoint and endpoint, into the midpoint formula.

[FORMULA: The midpoint formula is

M = (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})

where M is the midpoint of a line segment with endpoints at (x_1, y_1) \text{ and } (x_2, y_2).

EXAMPLE: mid point (11, 12) and (19, 0)

M(x,\ y)=(\frac{19+11}{2},\frac{0+12}{2})

Step 5: Simplify the fraction.

Step 6: Compare the x and y terms of LHS and RHS to find the coordinates of other end point.