coordinate geometry – straight lines - In ∆ABC, the coordinates of A and B are (–1, 4) and (11, 12) respectively and ∠ABC = 90°, as shown in the diagram above.

Krishna (last edited 5 years ago) (Expert, Educator @Qalaxia)

Step 1: Note down the given values and understand hints given

Step 2: 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 3: 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)

(11, 12) = (\frac{19 + x_2}{2}, \frac{0 + y_2}{2})

Step 4: Simplify the fraction.

Step 5: Compare the x and y terms of LHS and RHS to find the coordinates of other end point.