Solution:
Given: PQ = QR because Q (0, 1) is equidistant between P (5, – 3) and R (x, 6).
Step 1: Using the distance formula, calculate the distance between PQ and QR.
PQ
QR
Step 2: Use PQ=QR
To omit the square root, square both sides.
![\[41\text{ }=\text{ }{{x}^{2~}}+\text{ }25\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-5b0d06608613addbb06a0fc4187c7265_l3.png "Rendered by QuickLaTeX.com")
![\[{{x}^{2~}}=\text{ }16\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-86a05411276e106fb0ee329789a635fe_l3.png "Rendered by QuickLaTeX.com")
![\[x\text{ }=\text{ }\pm \text{ }4\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-481e71b85884c777f97b0693b42d58cc_l3.png "Rendered by QuickLaTeX.com")
![\[x\text{ }=\text{ }4\text{ }or\text{ }x\text{ }=\text{ }-4\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-11bf987358ebb4d5349f2007a5dbe12f_l3.png "Rendered by QuickLaTeX.com")
R (4, 6) or R (-4, 6) will be the coordinates of Point R.
If R (4, 6), then
QR
PR
If R (-4, 6), then,
QR
PR