Math Problem Statement

Find the equation of the straight line QR, given points Q and R from the diagram of a parallelogram on a Cartesian plane.

Solution

The problem asks to find the equation of the straight line QRQR given points QQ and RR in the diagram.

Here is the process to find the equation of line QRQR:

  1. Determine the coordinates of points QQ and RR:

    • Point RR is given as (7,4)(-7, 4).
    • For point QQ, let's assume we calculate it from the diagram (it appears near P(3,7)P(3, 7)), but we need to estimate based on the symmetry of the parallelogram and additional information if available.
  2. Find the slope (gradient) of line QRQR: The slope of a line through two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is calculated by the formula: m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1} Using coordinates Q(xQ,yQ)Q(x_Q, y_Q) and R(7,4)R(-7, 4).

  3. Equation of the line: Once the slope mm is determined, the equation of the line can be written in the point-slope form: yy1=m(xx1)y - y_1 = m(x - x_1) Substituting mm and one of the points (either QQ or RR) into this equation will yield the equation of the line QRQR.

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Linear Equations
Slope

Formulas

Slope of a line: m = (y2 - y1) / (x2 - x1)
Point-slope form of a line: y - y1 = m(x - x1)

Theorems

Equation of a Line
Slope Formula

Suitable Grade Level

Grades 9-11