188k views
3 votes
Consecutive sides of a square are perpendicular; therefore, QR 1 SQ. Find thevalue of x.

Consecutive sides of a square are perpendicular; therefore, QR 1 SQ. Find thevalue-example-1
User Ben Kane
by
8.1k points

1 Answer

3 votes

SOLUTION

Since QR is perpendicular to SQ, then,

Let the grdient of the line QR be m1 and the gradient of the line SQ be m2.

Since QR is pendicular to SQ, m1 x m2 = -1


\begin{gathered} \text{From m = }\frac{y2\text{ -y1}}{x2\text{ -x1}}\text{ } \\ m1\text{ = }\frac{1\text{ - 3}}{7\text{ - 3 }}\text{ = }(-2)/(4) \\ =\text{ }(-1)/(2) \end{gathered}
\begin{gathered} m2\text{ = }\frac{3\text{ - }1}{3-\text{ x}}\text{ } \\ m2\text{ = }\frac{2}{3\text{ -x }} \end{gathered}
\begin{gathered} (-1)/(2)\text{ }*\frac{2}{3\text{ -x }}\text{ = -1 } \\ \frac{-2}{2(3\text{ -x)}}\text{ = -1} \\ \frac{-2}{6\text{ - 2x}}\text{ = -1 cross multiplying, we will have } \\ -1(6\text{ - 2x) = -2 } \\ -6\text{ + 2x = -2 } \\ 2x\text{ = -2 + 6} \\ 2x\text{ = 4 } \\ x\text{ = 2} \end{gathered}

Therefore, x = 2

User Askaroni
by
8.5k points

Related questions

1 answer
2 votes
206k views
asked Jun 20, 2024 204k views
Denis Tarasov asked Jun 20, 2024
by Denis Tarasov
8.6k points
2 answers
2 votes
204k views