Ready to solve?
Click "Step 1: Sketch" below to begin applying the SOS framework.
Step 1
Sketch a Rough Diagram
First, we plot the given vertices roughly on the coordinate plane to visualize the triangle.
- Point O(0, 0) is at the origin.
- Point P(0, 60) lies on the y-axis.
- Point Q(96, 48) is in the 1st quadrant.
Step 2
Observe if there is any vertical or horizontal line
Look closely at the sketch. Notice that side OP lies on the vertical y-axis.
Since the orthocentre lies on the altitude from Q to OP,
let the orthocentre be H(x, 48).
Step 3
Use Slopes to find the remaining coordinate
Slope of OQ =
1
2
Slope of PH =
48 - 60
x - 0
Since OQ ⊥ PH,
1
2
×
-12
x
= -1
-12 = -2x
So, the x-coordinate of the orthocentre is 6.
Summary
-
SSketch a Rough Diagram
-
OObserve horizontal or vertical lines
-
SUse Slopes to find coordinates
Diagram will appear when you begin