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2023 WAEC Further Mathematics Theory P is the mid-point of \(\overline{NO}\) and equidistant from \(\overline{MN}\) and \(\overline{MO}\) . If \(\overline{MN}\)...

Further Mathematics
WAEC 2023

P is the mid-point of \(\overline{NO}\) and equidistant from \(\overline{MN}\) and \(\overline{MO}\) . If \(\overline{MN}\) = 8i + 3j and \(\overline{MO}\) = 14i - 5j, find \(\overline{MP}\) .

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Explanation

\(\overline{MN}\) = 8i + 3j

\(\overline{MO}\) = 14i - 5j

Consider ∆MON

\(\overline{MN}\) + \(\overline{NO}\) = \(\overline{MO}\)

\(\overline{NO}\) = \(\overline{MO}\) - \(\overline{MN}\)

\(\overline{NO}\) = 14i - 5j - (8i + 3j) = 6i - 8j

Since P is the midpoint of \(\overline{NO}\), then

\(\overline{NP} =\frac{1}{2}( \overline{NO} )\)

\(=\frac{1}{2}(6i - 8j) = 3i - 4j\)

Consider ∆MNP

\(\overline{MN}\) + \(\overline{NP}\) = \(\overline{MP}\)

(8i + 3j) + (3i - 4j) = \(\overline{MP}\)

\(\overline{MP}\) = 8i + 3i + 3j - 4j

∴ \(\overline{MP}\) = 11i - j


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Post-UTME Past Questions - Original materials are available here - Download PDF for your school of choice + 1 year SMS alerts
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NECO June/July 2024 - Get offline past questions & answers - Download objective & theory, all in one app 48789
WAEC Past Questions, Objective & Theory, Study 100% offline, Download app now - 24709
Post-UTME Past Questions - Original materials are available here - Download PDF for your school of choice + 1 year SMS alerts
NECO June/July 2024 - Get offline past questions & answers - Download objective & theory, all in one app 48789
WAEC Past Questions, Objective & Theory, Study 100% offline, Download app now - 24709
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