coordinate geometry – straight lines - The points A(1,7), B(20,7) and C(p, q) form the vertices of a triangle ABC, as shown in the diagram. The point D(8, 2) is the mid-point of AC.

Krishna (last edited 4 years ago) (Expert, Educator @Qalaxia)

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

Step 2: Substitute the values of midpoint and given 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 3: Simplify the fraction.

Step 4: Compare the x and y terms of LHS and RHS to find the coordinates of other end point.